Democrats' convention is over, but its embers may ignite hot campaign.

Bay State Democrats may not be the big happy family their leaders would have them appear, despite the relative tranquillity at the party's preprimary convention last weekend.

None of the four Democrats whose candidacies for US Senate survived Saturday's convention can take comfort from all the politicking behind the scenes.

The convention accomplished little toward the winnowing-out process - its major reason for being. Delegates, while unwilling to scrap the rule requiring a candidate to get 15 percent of the delegate support to continue his quest, in effect circumvented the rule. In the contest for the seat being vacated by Democrat Paul E. Tsongas, this was accomplished by vote-switching between ballots.

As a result, Massachusetts Secretary of State Michael J. Connolly, who polled 7.9 percent (317 votes among 4,007 delegates) on the convention's first round, remains in the running for his party's senatorial nomination in the Sept. 18 primary. This means the field of Democratic aspirants to the US Senate has dropped not to three but to four - a situation that may provoke a more divisive campaign.

If nothing else, the doubling of his support on the second convention ballot spared Mr. Connolly a bit of political embarrassment, at least for now. But even with the support of 673 delegates on the second round, the Boston Democrat has a long way to go to project himself as a strong contender.

Many of the delegates at the Democratic gathering in Worcester are liberals who, understandably, may have found the candidacies of US Rep. James M. Shannon, the endorsee, and Lt. Gov. John F. Kerry, the runner-up, more philosophically appealing.

Connolly is not a conservative, but in some respects he is less of a liberal than Mr. Shannon and Mr. Kerry. If Connolly's candicacy had ended last weekend, his supporters may have been more likely to swing to David M. Bartley, rather than to Shannon or Kerry. Mr. Bartley, former speaker of the House and now president of Holyoke Community College, is perceived by many of his fellow Bay State Democrats as being a bit more conservative than the others.

Bartley could not have expected to do much better than the 24 percent delegate backing he managed. After all, the lion's share of the delegates, if not liberal-leaning, were supporters of Gov. Michael S. Dukakis. And despite the governor's neutrality in the senatorial tussle, he does not view Bartley - who served as secretary of administration and finance under former Gov. Edward J. King - as a political favorite.

If Connolly had been winnowed out of the contest, the smaller field of candidates could have worked to Bartley's advantage. He could have made political hay among conservative Democrats - and even among many moderates - in the September primary. At the same time, he could probably count on some support from liberal Democrats, especially those with legislative ties who remember his strong voting record in behalf of liberal-oriented causes.

Failure to win the convention endorsement has to be viewed as a major blow to Lieutenant Governor Kerry, who is probably best known among the delegates across the commonwealth. Of the three top Democratic contenders, he is the only one with statewide ballot exposure, having topped a crowded field to win his party's 1982 nomination for his current office.

His loss to Congressman Shannon, 53.3 percent to 46.7 percent on the fourth ballot, came despite a well-orchestrated effort to sell his candidacy to the delegates. Kerry, who had been leading in most preconvention polls, blames his loss on Bartley supporters being persuaded to shift to Shannon after their candidate withdrew from his quest to seek the party endorsement.

It may never be known if the lieutenant governor was a victim of some shrewd behind-the-scenes maneuvering by his opponents. It could be that, in most instances, delegates who went from the Bartley bandwagon to Shannon's found the congressman's candidacy more appealing than Kerry's.

On the first three rounds, Shannon held a delegate edge over Kerry: 36.1 percent to 31.9 percent on the first; 34.2 percent to 28.5 on the second; and 41 .8 percent to 38.1 percent on the third.

Kerry's suggestions aside, the Bartley withdrawal from endorsement competition appeared to boost delegate support of both remaining contenders. Congressman Shannon had slightly more than the disappointed lieutenant governor.

From Shannon's standpoint, winning the convention endorsement was a sweet victory, although a fragile one. In addition, it places him in the position of front-runner, where he is an easy target of all three opponents.

More important, any suggestion that Democratic activists at the Worcester proceedings represent the party's Bay State ranks is misleading, if not inaccurate. Democrats whose ideological leanings are more in the direction of former Governor King were neither seen nor heard at the convention.

This is not the fault of those in charge. Every effort was made party leaders to prevent freezing anyone out. Those supportive of Governor Dukakis, including members of the politically active Massachusetts Teachers' Association, were simply better organized when delegates were elected.

The convention's richest legacy may not be the endorsement of a senatorial candidate but the scene-setter for a long, hot summer of political infighting in a campaign dominated personalities rather than clear-cut issues.

One things is sure: Massachusetts voters will be seeing a lot more of four senatorial hopefuls who have been at it since January - and they may wear out their political welcome long before the September primary.