Hate to burst your bubble, but as an amateur musician I fear this would backfire, or at least fail to result in any improvement in playing ability. Silence and time are absolutely critical to playing music. By analogy, measuring 'time spent drawing bow across strings' would be as useful to a violin student as 'time spent pressing foot on accelerator' would be to a driving student!

From my own experience learning to play the organ, I have improved least when I play relatively fluidly, practising with music well within my abilities. On the contrary, the most improvement has come when I've slowed down, allowed myself to count the timing, repeat sections, read the sheet music more carefully or even just take a break entirely. So although silence won't improve one's playing by itself, I think it's a natural by-product of an effective studying technique that, if at all possible, shouldn't be discouraged with such a timer.