Philosophy of perfect inter-sample interpolation
By the fundamental notions of signal processing, we can state that, a perfect intersample interpolation of a given perfectly bandlimited signal from its samples is not possible due to the fact that a perfectly bandlimited signal would be infinetely long whose infinite many samples are required to compute any one single interpolated intersample, hence impossible.

That being said, i.e. that the impossibility of obtaining infinite duration samples, a practical answer would be yes if you would allow an upperbound on the acceptable interpolation error, such as lower than the roundoff error within a digital system. This will be a truncation error whose spectral manisfestation is spectral smearing due to the convolution of the truncating window's frequency spectrum with that of the true spectrum of the bandlimited signal (i.e. multiplication in time, convolution in frequency)

Also a tradeoff can be sought that, instead of a perfectly bandlimited signal, you can work with bandlimited enough signal whose aliasing error is within acceptable bounds, just as in the previous paragraph, in this case you wont need infineteley many smples, but there will be spectral overlap.