It would be easier to paint over the ply with the paint, try and make sure you seal all the edges, and make sure the wood is sealed prior to painting
Also use a brush as it doesn't clump, and once finished is a good idea to use a rubber mat as well,, as this will stop the paint from chipping, and prolong the life of the paint.
It is all down to good preparation, and you should give yourself at least a couple of days to do the job.