Yes, you should be fine for now with the old PSU.
You will want to change it in the future though, how long depends on how old it is. I used a 3 year old SeaSonic for almost a year before I got a new one when I upgraded.
You'll want to upgrade it at some point. No matter how good the capacitors are, they will get old and weak eventually. I would recommend a 600W to lessen the strain on it.