If I sample the output for constant output(accelerometer is not
moving), can I say anything about signal to noise ratio by looking at
You can only say what the noise is. Here's how you compute the noise RMS level based on taking many samples: -
Picture taken from here.
Subtract your static DC offset from the noise samples before squaring each term. Alternatively, if your noise is gaussian in nature you can estimate the RMS value from the peak values: -
A reasonable approximation would divide the p-p value by 6.6 to get RMS. Picture directly above taken from here. Here's a picture from TI that shows the reverse calculation: -
Regarding your signal, if you know what performance your transducer gives i.e. its transfer function then you can assume that a signal is present in the noise you have measured and calculate SNR.