The timer must really, really run fast compared to the bandwidth of the noise generator to keep down the aliasing between sequential samples.

If the timer runs at 1MHz it will only have ticked 1000 ticks in 1ms so each interrupt would produce very few bits of random data to add to the entropy pool. Besides limiting the amount of random numbers that may be generated per second, it will be needed to perform post-processing of the timer reads. Either a few of the least significant bits may be picked up and used, or a good one-way hash should be used.

So if little random data is needed, then the noise data from the may accumulate until needed.

If much random data is needed, then the noise data from the hw would probably only be enough for the internal and secret state of a PRNG.