There's no reason that aquifer influx cannot be taken into account using FMB methods. There's nothing arcane about FMB, it is simply a method to take producing rates and pressures and infer what the reservoir pressure is. From then its a standard material balance calculation.

Now, whether FMB (or indeed standard MBal) methods can be used to infer aquifer influx - deconvoluting the rate/pressure behavior to point to aquifer influx over (say) low perm contribution in something approach a unique solution is highly questionable in my mind. Strongly suggest mapping out a couple scenarios and match them all, then talk to your friendly geos and the like to see what scenario seems closest to the truth.