After some digging in the manual (downloadable from the Boss site) I found that the current draw from the ME-50 is 120mA, since your PSA adapter can put out 200mA, that should leave 80mA spare current and should work just fine.
Unless you want to daisy chain a compact pedal alongside the ME-50 from the same adaptor, then you'll have to figure out how much current the pedal draws before you reach the limit of 200mA.
In that case you'll either need a bigger adaptor or a second one just for powering your pedals.