I'll be a contrarian, and say it is certainly possible, but I think it is unlikely the cause is as you describe. And there is certainly not enough information in your post to decide one way or the other....
Some diagnostics for you:
Is the alternator internally regulated? (An alternator without a "smart" regulator
will never drop its output so low that the tach wouldn't work)
If you rev the engine
and the tack goes to zero, does it resume working if the rpms drop again? This would indicate that the belt is slipping under the heavier load of higher RPMS)
If you start the engine and rev it up within a few minutes, does the tach response fail? (output even from smart regulators is high for a default period right after start up.)
Finally, you can test your proposed cause by setting things up so the tach is not working, and then turning on something that draws current
. This would force the alternaor to be energized. If the tack still stays off, you should look for the problem elsewhere.
I'd bet the problem is with the belt. Once they start slipping at higher rpms, they can lose "bite" on the pulley and keep slipping.