The CX-600M yes, the non-modular CX-600, no. Both are initially powerful enough. Both were made by CWT for Seasonic. They don't use the same parts though; the non-modular CX-600 contains some inferior Samxon capacitors that don't like heat and are known for early failure. For that reason, I would not use one in a gamer.
It will weaken more rapidly than a quality PSU will, and/or lose its ability to properly reduce ripple and noise on its rails, possibly leading to instability or even component damage over an extended period of time.
Modular means either none (full modular) or only some (partial modular) of the cables are permanently attached to the PSU. Any not permanently attached are inserted into sockets. This allows you to use only the cables your system needs. Electrically there is no significant difference between them (despite some ancient and misleading marketing claims to the contrary). Aesthetically, it means you'll have fewer cables to stash out of sight and out of the airflow in your case.
How about the CX-500M? Though smaller, it is certainly enough, and it was built with all-Japanese capacitors so it should last.
Keep a non-modular CX from running hot all the time (make sure it has good airflow, e.g. your case has some intake fans, not just all exhaust), and it ought to last at least a year or two, maybe more.