[lvh]

There is serious disagreement between serious legal scholars (Moglen, Rosen) about what kind of cooperation between components would trigger (A)GPL virality clauses. Linking counts according to one, but not the other; IIUC everyone agrees subprocesses don't count.

So, assuming said company would not want to AGPL their code (and assuming they don't distribute binaries), that choice would imply some technical decisions they would presumably not be very happy about, but overall: no.