Not if they are all on the same frequency and unsychronised.
Consider the same thing happening on an HF or VHF voice channel. If a hundred pilots press their buttons at the same time and transmit a long message, the result is just noise. The fact that they each precede their message with a callsign doesn't help at all. That is why there is a strict allocation of frequencies and a protocol to define when and how to transmit. Similarly data transmissions require their own protocol which may well be IP based but needs a complex hierarchy and infrastructure.
Regarding the store-and-forward idea, this has been proposed earlier in the thread. Like other suggestions it could be done, but requires a whole new generation of equipment that would be (a) very expensive and (b) difficult to retrofit in the existing fleet.