Well, 48-Volt phantom powering allows for a tolerance range of +/- 4 Volts, but I suppose you mean voltages even lower than that. The answer is that many 48-Volt microphones will still put out a signal of some kind at lower voltages, but their headroom and dynamic range may well be compromised--in some cases quite drastically. You might find that the microphone seems to have lost sensitivity, gained noise, and that it overloads badly on loud sounds. During a live performance is NOT when you want to be finding that out.
There are plenty of microphones that can operate on any of a wide range of voltages (e.g. 9 - 52) without loss of performance, though generally those are really 12-Volt phantom-powered microphones that can tolerate the higher voltages, and that simply throw the extra energy away as heat.
In any event no sane manufacturer would ever claim that their mike needs 48 Volts if it really doesn't, since that would be to their disadvantage in terms of sales. So if they say it, I suggest that you believe it (or act as if you believe it) unless there is solid evidence to the contrary.
--best regards