It is inconsistent with FIFA regulations.
FIFA Regulations on the Status and Transfer of Players. Article 18, paragraph 2:
The minimum length of a contract shall be from its effective date until the end of the season, while the maximum length of a contract shall be five years. Contracts of any other length shall only be permitted if consistent with national laws.
I'm not sure how much of an out is provided by that second sentence. I don't even know if it refers to civil labor laws or local country soccer federation laws. If MLS had an exception to this FIFA rule I expect we would have seen it used to sign replacement level stop gap players until summer and then replace them in the more active summer window, but I cannot remember that ever happening.
This rule is part of the Lampard fiasco lore.
First, NYCFC/MC/CFG told us he signed with NYCFC (lie) and was loaned to MCFC for a half Premier League season (lie).
Then when ManC decided to keep him, people asked why MLS would agree to extend the loan.
So CFG had to admit that Lampard had not signed any MLS contract to that point. They claimed he had a half-season contract with Man City (lie) and they were extending it.
But some clever UK sports reporters pointed out first-half-season contracts are illegal. You can of course sign someone for the second half but not the other way round. Only then did CFG admit that Lampard had been signed to a full season contract with Man City the entire time.
It's possible that MLS or US leagues generally are exempt from the FIFA reg under the "consistent with national laws" clause, but I also wonder if, as with Lampard, there is something to the Rodriguez deal we are not being told. Probably less nefarious. Like maybe he is signed to a full year but he and Minnesota have a side letter agreeing to let him out after the World Cup. It might not be enforceable but it's their understanding anyway. The deception would then exist to temper fan expectations.