For peace of mind If the top can be removed fairly easily to gain access to the areas with rust then that is what you should do.
It will take longer, but you will have a better finished product, especially if it is something that you know may cause issues further down the road.
There are products out there to tackle rust, Spray can treatments, acid etching.
You can always treat the areas after paint with rust check/fluid film type products as well to slow the process.
Try and eliminate any areas where water can enter in the future and also create drain points for water that does enter.
