It would be far less appropriate to deny him his right of free speech. It would also encourage democratic behaviour by providing insight to issues by allowing him to express his side of events and opinions to a wide audience. Denying him a platform to speak is not part of his suspension.
No, he might make things worse. I think the player should be shut out from all media during an suspension. I really feel that if he is truly remorseful for the mistake then he needs to take time away. I don't feel that letting him talk to anyone helps the team at all.
They should not allow this man to talk on TV during his suspension. Suspensions are punishments, not to be forays into exposure for attention. There is no reason to have him on TV. Just let him get through the banishment first, then treat him normally again after it is all done.
Jameis Winston should not be allowed to talk on television during his suspension. It sends inappropriately mixed messages to both punish him and give him media attention. Additionally, in the context of sexual assault charges that are still being investigated, his comments are potentially very damaging indeed. Caution is best when an ongoing investigation is underway.