what affect, if any, does this have on the cooling of the avionics ventilation?
Some aircraft types have electrical loadshedding during start under certain conditions. E.g. the 767 loadsheds all galley and utility busses when starting the first engine on the ground (with the APU generator as a single power source). If certain equip cooling fans are powered by these busses, then you may temporarily lose this cooling during start.
Looking at wiring schematics, the 767 engine start loadshedding circuit involves start relays (K10250 or K10247) and auxilliary contacts on the APB (Aux/APU Power Breaker "C905"), the APU Bleed Air Supply Control Valve relay (K23) and the engine GCBs.
In your scenario, you say there is no bleed available. Is this because APU is not running? If this is the case, then there should be no loadshedding because the APB will be open (if we are talking about 767's). If the APU is running, but APU Bleed is selected OFF (K23 de-energised), then, again, there should be no loadshedding (NB: These circuits are fairly complicated, so it's my best guess
)
Regards
NSEU