If you only want to reconstruct your signal, as perfectly answered by @hotpaw2, the answer is no in general, especially if you have finnite length windows. But I do not see the point of performing analysis and synthesis without processing in the middle.
If you do perform some processing or detection inbetween, then errors in reconstruction (ripples, leakage) can become negligible, especially if you use some amount of oversampling and use optimized inverses.
An option though: downsample your sample first at a $2/N$ rate, and you can use the DFT filterbank on the full bandwidth, yet at a reduced rate.
[EDIT] After your mail, it took me a while to understand... something. Let me try to rephrase it (and tell me if wrong). You have a 16-channel analysis filter-bank. You keep the first 2 channels, $c_1$ and $c_2$. You have a 16-channel analysis filter-bank, and you want to split it into two polyphase components $d_1$ and $d_2$. From what I understand, both A and S frequency comments won't match.
Yet, you can try to perform an implementation, input a random noise, see what happens, and report the results here.