Can my 16 year old son recieve baseball bats, gloves, etc.. from a major equipment company to sponsor their equipment without signing a contract.

If you're asking about NCAA eligibility, I believe that this would make your son ineligible to play NCAA college sports.  I can't see how it would matter if the agreement was in writing or not. If you're asking whether the equipment company would agree to this, I doubt it.  Contracts with minors are voidable by the minor.  That means your son would be able to opt out of the contract whenever he wanted to, for a better deal of whatever reason, as long as he was a minor.  The company is going to want a signature from one or both parents.