No, the actual phrase that is commonly used for this exact scenario is "mess around" and not "mess somebody around".
"To mess someone around" is exactly what Michael Harvey said in his answer. From Cambridge, "mess sb about/around" means to treat someone badly. This is somewhat close to "mess somebody/you up" which means to cause someone to suffer emotional and mental problems. This is something different than what you are looking for.
From what you say, it seems like the guy is uncertain about this. While the woman is fully committed, the man isn't. He however continues to see this woman. This means he is spending time with her (and possibly having sex with her).
The phrase you want is "mess around" which means to spend time doing various things that are not important, without any particular purpose or plan (Cambridge). This in your case easily means spending time with someone without fully committing into the relationship.
From the Free Dictionary: Mess around with (someone or something)
(3) To engage in aimless recreation or frivolous time-wasting with someone or something; to fool around with someone or something.
(5) To engage in casual sex acts with someone.
- Betsy and I are just messing around with each other, which is great because I don't want a serious relationship anyway.
Note that context is very important.
"Mess around (with sb)" has a set meaning too. If a married man or woman messes around with someone, they have a sexual relationship with someone who is not their wife or husband (Cambridge).
But the phrase is commonly used for just casual relationships (where one is not committed), at least from what I have seen.
You can also use "fool around with".
1: to use or do (something) in a way that is not very serious
3: to have sex with (someone who is not one's husband, wife, or regular partner)
Then there is the phrase "string along".
If you string someone along, you deceive them by letting them believe you have the same desires, beliefs, or hopes as them.
From the Free Dictionary,
(4) To cause someone to remain in a state of uncertainty or expectation, usually to achieve some end.
She's not stringing you along, Jim—she's just being your friend, but you're trying to pretend there's a chance she likes you romantically.
She was in tears when she found out that he'd just been stringing her along.