Sampling Rate and SNR Assume I have a signal that oscillates between 10KHz and 9Khz every 500msec (Change happens linearly, so at t=0, it is 10KHz and it goes to 9.5Kz at t=250msec and 9KHz at t=500msec and frequency start to increase and goes back to 10KHz at 1 sec and this goes on)

Assume I sample this signal at 50Khz and I do fft to find out what's the frequency. But due to sampling rate, I have to accumulate some samples where the interest frequency is slowly shifting. 

If I were to sample at 500KHz or even 5MHz, can I get a better SNR? (The assumption here is that I can sample for a shorter duration -still several cycles of the target frequency in time domain- and this will provide a less spread signal in a given time and better fft snr. )

My gut tells me, this won't help but I like to ask the crowd.
Your instincts are right. You won't increase SNR by increasing sampling rate because you also have more noise samples. The overall signal energy and noise energy does not depend on sampling rate.

But, I believe you are mixing up two problems. In your case the frequency is not constant, therefore Fourier based analysis yield less than optimal results. Your problem is in the signal itself, not the signal to noise ratio. You can have a look at the high-order ambiguity function (try this or that) or the Wigner-Ville transform. Those are more suitable for linearly changing frequency.