B737-700 FLT CREW IS CONCERNED WITH PUSHBACK PROCS FROM THE GATE AT BWI.

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DOORS CLOSED; READY FOR PUSHBACK AT GATE. CALLED 'A' PUMPS OFF; BRAKES SET TO GND PERSONNEL ON HEADSET. LONG PAUSE; THEN RECEIVED MESSAGE; 'THIS WILL BE A 3-MAN PUSH.' I REPEATED; ''A' PUMPS OFF; BRAKES SET' AND RECEIVED REQUIRED 'SAFETY ZONE CLR; DOORS CLOSED.' TOLD THE PUSHBACK CREW ''A' PUMPS OFF; BRAKES RELEASED; CLR TO PUSH; WILL TURN TWO FIRST.' GND PERSONNEL INDICATED SAFE TO START TWO; WHICH WE STARTED MOTORING. AS PUSHBACK STARTED; ACFT STARTED L (MY L) TOWARD THE JETWAY. THE ACFT STOPPED; AND I ASKED 'DO I NEED TO SET THE BRAKES? DO YOU WANT ME TO ABORT THE START?' NO ANSWER. I REPEATED THE QUESTIONS AND ASKED; 'WHAT IS GOING ON DOWN THERE?' A NEW VOICE (THE TRAINER; I THINK) CAME BACK; 'NO; DO NOT SEE THE BRAKES. YOU MAY CONTINUE THE ENG START.' WE STILL DIDN'T MOVE MUCH; THEN A LITTLE; THEN STOPPED AGAIN AND I AGAIN ASKED THE QUESTIONS ABOVE (I HAD THE ENG SPINNING ON THE STARTER BUT HAD NOT YET ADVANCED THE FUEL AS I DIDN'T LIKE THE SITUATION). SAME ANSWER AS ABOVE; THEN PUSH FINALLY RE-COMMENCED; CONTINUING TOWARD THE JETWAY AND BACKWARD. THE OPS AGENT WAS STANDING ON THE LIP OF THE JETWAY WITH HIS THUMB UP IN AN 'OK' SIGNAL AS THE PUSH CONTINUED. WE WERE SO CLOSE TO THE JETWAY I COULD NOT TELL IF WE WOULD CLR IT OR NOT BUT I DID NOT FEEL I COULD CTL THE SITUATION VIA THE HEADSET. WE DID CLR THE JETWAY WITH NO DAMAGE AND STARTED THE ENG AND SUBSEQUENTLY #1 AND FINISHED THE PUSHBACK NORMALLY. IN HINDSIGHT; I SHOULD HAVE ABORTED THE START AND REQUIRED THAT THE ACFT BE PULLED FORWARD TO CTR ON THE LINE AND MADE THEM START OVER. I DO NOT FEEL THAT TRAINING SHOULD BE DONE WITH A LOADED ACFT BEING THE FIRST ACFT A PERSON PUSHES BACK; WHICH SEEMED TO BE THE SITUATION TODAY.