Yes, it is a possibility--but even if the two entries are connected (may be, may be not), they only indicate that Alexander was commissioned to buy a rifle and that, when he got to Lancaster, he bought that rifle from Dickert. The entries don't say that he receives money while in NC to buy, specifically, a Dickert rifle. The initial entry, that is, specifies in great detail the size of the rifle he wants; it could have easily have said "from Dickert" if that's what he'd been commissioned to purchase.
So, yes, it's possible that Dickert's name was known in North Carolina and somebody there wanted a Dickert rifle (and commissioned Alexander to buy one). But it's by no means certain that that's what these diary entries indicate...
I suppose the key question (for me) is: did Alexander know to go right to Dickert to buy the rifle he'd been tasked to buy? If so, then I'd agree that Dickert's name was known in North Carolina at the time. Or: did he get commissioned to buy a rifle and, once arriving in Lancaster, get directed to Dickert? Hard to know. Probably the first option, if the two entries are connected.
Just my two cents.