I don't quite follow what you're asking.
I know what he’s asking about… It’s something I’ve been asking about for quite a long time (>5 years): forcing a *measure* or even *group of measures* (in OP's case, a single measure) to stretch to accommodate another grob (in OP’s case, a TextScript), rather than the current behaviour ("stretch the current moment"). The problem is particularly acute in parts with lots of tempo markings over multi-measure rests, which don’t tend to stretch accordingly.
* The action of \textLengthOn extends the length of the moment in time at which it occurs.
*All notes which occur at a later musical moment will be displaced to the end of the text.
It would be nice to be able to arbitrarily set the duration of the moment that would (if necessary) be stretched.