IN ITS REPORT to Sen. Patrick J. Leahy (D-Vt.), the General Accounting Office has looked at the District's downtown convention-center plan as skeptically as an old-fashioned banker might regard a small businessman's request for a very large loan. The GAO expressed three pricipal concerns:

There is no gurantee that a high volume of convention business, and the resulting economic and tax benefits for the city, will materialize.

Construction costs might well run over $110 million even if no complications arise; relocation problems and lengthy environmental reviews could upset the tight timetable and push costs up several million or more.

The city might not be able to attract a highly qualified manager to promote, market and administer the center effectively. GAO did not consider the city's ability to coordinate the project with redevelopment in the Mount Vernon Square area, but that, too, belongs on any list of major uncertainties.

All these concerns boil down to one: whether this ambitious undertaking can be managed well enough at every stage by the city and the proposed convention-center board. Obviously there is no way to get absolute assurances in advance. On the other hand, decisions about the project need not be based on faith - or lack of faith - alone. Congress and the community can learn a lot from the record of the city's performance on other projects and the preliminary convention-center work now under way.

That record, as we see it, is mixed. The District has managed to build some large facilities, notably the central library and the new jail, without great overruns or long delays. The local handling of recent redevelopment projects, on the other hand, does not inspire enormous confidence. Moreover, the center's designers so far have not shown enough interest in innovative links between the center and the community. Possibilities such as rooftop recreational facilities and street-level shops have been advanced mainly by others, including Councilman William R. Spaulding and architect John Wiebenson.

All this leaves us - and, we suspect, many in Congress and the community - somewhere between the optimism of the project's advocates and the pessimism implicit in the GAO report. Fortunately, there is one good, immediate test of the city government's capacity to get organized: how fast the mayor and council can put together the tax package and management structure that are vital to the entire plan. The council has set itself a deadline of October 1. That is too late. Congress will have to decide this summer about the first $27.7 million in local borrwing. Many legislators may be reluctant to approve that if the city has not actually imposed the business and hotel taxes - and, even more important, set up a strong independent board to run the center. A lot depends, therefore, on whether the mayor and the nine council supporters of the project can bestir themselves and reach agreement on these measures expeditiously. If they can't, the promoters of the enterprise may find themselves demanding from the skeptics among us more blind faith in their projections and promises than they can resonably expect.