It is an interesting question and it is hard to be certain of the answers.
It clearly must have varied depending on what imitations we are talking about.
Imitations of the coins of the 318-320 period - i.e the VLPP and its bretheren - are very odd. The official coinage jumps in 318 from approx 1.5% fineness to approx 4% fineness and their is likely a fiduciary re-valuation the results in 318 being a "barrier" in hoards. I believe that most imitations have very low fineness - approx 0.5% - but maintain the weight range. They should therefore be intended to deceive and to yeild some measure of profit as their intrinsic value would be a fraction of the ones with 4% silver (given approx 1:100 AR:AE value of the time). However, the designs of many are so barbaric as to have made identification
rather easy. So what gives??
By contrast, the imitations of the 330-341 period - i.e. GLORIA EXERCITVS
and its bretheren - come in both regular weight and reduced weight. Now with fineness values averaging approx 1.3% 330-336 and 1% 336-341 the coins had a low intrinsic value anyway so even a drastic reduction of weight would not really altar the overall intrinsic value by as much as in earlier coinage.
So how to explain the under-weight imitations? People have tried in different ways.
Some thought that they were struck much later than the original types and the reduced weight related to the by-then reduced standard - i.e. GLORIA EXRCITVS struck in the 5th or even 6th century. This arguement has been de-bunked by hoard evidence or co-circulation.
Another theory is that they traded by weight - tied up in bags - so it did not matter how heavy the individual coins were (nor incidentally what their design looked like) just what the overall weight was. I believe that the challenge with this theory is that there is no evidence of this untill well after the mid-4th century.
Then of course there is the theory you mentioned that they traded at their "face" or fiduciary value regardless of weight, and thus intrinsic value. Given that most imitations seem to occur in relatively limited geographic area - i.e. not empire wide - and for relatively brief periods and are often linked to shortages of regular coinage I would not be surprised if this was the correct explanation. And even though bronze / aes was valuable the difference in the intrinsic value between a 1.7 grams late official GLORIA EXERCITVS
and a 0.85 gram (1/2 weight) imitative was really not that much when they were already likely overtarriffed in terms of their fiduciary value.
Perhaps they were a sort of parallel to 3rd century provincial coinage - circulated at an accepted rate in certain areas and circumstances but not so accepted everywhere.