Is it possible to use Luminen Blast (with BS) in melee?

Theoretically, no; unless a ranged attack says it can be used in a melee, it can't.

Assume it takes a half-second or so of staying static to draw the charge from the potentia coil and aim whatever focusers are used - that's not an effective weapon when someone is within a metre and trying to repeatedly punch you.

the GM, of course, may rule otherwise.

Just use Luminen Shock for melee combat instead. I don't believe there's much difference between the effectiveness of the two (besides the possibility that your tech-priest has much higher BS than WS).