Band-limited signal recovery with finite bit depth
Quantization is a loss of information. So if you quantize a signal, you will never be able to reconstruct it perfectly.

That being said usually we can, in certain circumstances, assume that  quantization is a kind of noise. In these circumstances, assuming an N-bit ideal ADC with a full-scale sine wave as an input. 

$$SNR (dB) = 1.76 dB + 6.02N$$ 

So an ideal 16-bit AC would give you a dynamic range of about 98 dB. The hard question, is whether or not that's enough for your application. Unfortunately we cannot answer that for you.

Now, as to oversampling. If the quantization noise is not correlated, then yes oversampling can help you decrease the quantization noise, and thus increase the dynamic range in a certain frequency band. The rule-of-thumb is that oversampling by a factor of 4, then filtering, then downsampling by 4 is equivalent to adding another ADC bit, i.e. adding 6.02 dB to your dynamic range. 

However, sigma-delta ADCs also perform quantization noise-shaping which allows them to vastly increase their dynamic range in a certain frequency band. Combined with oversampling, this allows them to implement 24-bit and 32-bit ADCs.

For more information on sigma-delta ADCs https://www.analog.com/en/technical-articles/behind-the-sigma-delta-adc-topology.html