Indeed, with ACBC the "None" weight that automatically comes out of the standard ACBC setup (BYO, Screeners, Tournament) is a different animal that what comes out of a CBC. With the standard 3-section setup in ACBC, the None weight is actually the utility for the "not a possibility" alternative in the Screener section.
Some researchers like to add the optional "Calibration" section to the end of ACBC surveys (BYO, Screeners, Tournament, Calibration) and then ask our software to do the additional step (after estimating HB utilities) of calibrating the None utility so that it fits (in a least-squares sense), say, a 4 on the 5-point purchase intent scale for each respondent.
Regarding what is "allowed" in terms of size of the parameter, if using the standard None coming from the "not a possibility" option, it is whatever the MNL estimation allows within the HB estimation. In my experience, if I am using Summed Pricing with the piecewise function for price without monotonicity (sign) constraints on the price attribute, then the None weight can wander around quite a bit across the history of HB estimation.