A "check" is a negotiable instrument intended for immediate negotiating, NOT as a promissory note).One should also keep in mind that, in some jurisdictions, writing a post dated check and if it were to arrive at the issuing bank earlier than it was dated for, and assuming the account it was drawn on has insufficient funds to pay the full amount, it can be subject to a criminal investigation and possible charges being filed by locale law enforcement.
The law requires that certain steps be taken by the recipient of a “worthless check” before the State Attorney begins prosecution.
However, most banks -at their option- may either reject or negotiate a post dated check as if it has the current/past date on it.
Since most "post dated" checks are written due to the account they are drawn on not having sufficient funds to cover it, depositing a check before its intended written date is more likely to result in it being returned for insufficient funds.
That would depend on the trust between the parties, but it can apply to settle an outstanding debt.
As noted in another question, banks have different policies regarding post-dated checks before the post-date, although it seems most will accept the check as long as the check issuer hasn't contacted the bank.