No, but after he uses that bow in a crime, I'll have the Pawns register his Fake SIN as a person of interest to watchout for. And if he purchases another item send the Pawns to pick him up, since he just left a paper trail leading to himself. And while its possible that he'll just go in for a bit of questioning, if they find any other illegal gear on him, he'll be arrested.
Though, it might not escalate that quickly. I was just exaggerating to make the point.
But keeping things off the record is moderately important for professional criminals. So you probably want gear that's completely illegal, and not just stuff tied to your fake SIN.
It's a management of risk. A gun will leave a unique mark on any round it fires. If Joe Average (aka Razor McNail) brought a gun on a fake SIN and used it in a crime, then Joe Average may be wanted for questioning. Effectively that SIN is burnt. Worse, the shop might have a Trid recording of Joe/Razor. However, this is all beside the point! None of this is a point of dispute!
Whether or not a shop like
http://www.lancasterarchery.com/ exists near Joe/Razor, is also beside the point. These things are entirely ymmv things, up to individual GMs/groups to decide.
For those who already know my point, I apologise for belabouring it. However, it seems I have not been clear enough for some.
My position is: There are no mechanics by RAW to buy items, with availability, retail. I would have appreciated some.