Can use of zIIP impact need for more UBs under CICS?

We were running a trial of the zIIP Enabler for Natural Batch and encountered an error for the first time (NAT3218 and S0C4 in ADACICT). We always throughout the entire installation of Natural took the default NUBS value (100). My theory here is that with more batch throughput with zIIP enabled, there would be more general processor capacity available for CICS transactions, perhaps allowing the situation to exist where Natural under CICS needs more user blocks than ever before.

We found also that, though we thought we had CI833002 applied (ACI v833 zap addressing an issue with cleanup of UBs for ADAMODE processing), we did not. Chances are that this will prevent both the NAT3218 and the S0C4 abend, but I am still wondering if I need to increase NUBS as well, and even more so if we buy zIIP Enabler for Natural Batch permanently and even more than that if we also buy zIIP Enabler for Natural under CICS (as they are now licensed separately as of Oct 2017).

Thanks in advance!