Pitted rust on frame
Answer:  No.  There are no good quick and easy top-coat treatments for your situation.

The problem is that pitting is a loss of material.  The metal is gone already, and the non-smooth surface will hold and hide moisture even when it looks and feels dry.  The corrosion will not stop because you've painted it even with anti-rust paint.

Not-Good Answer You can paint on rust-converter, which will transform the red/brown rust oxide into a more stable black oxide with a white foamy layer on top.  Once its converted and dried, wipe off the white stuff and then paint.  This is only a slowing action, but if it slows the rust down by 10 years then that may be all you require.

Stripping the paint at a bead blaster or sandblaster will remove all the paint and decals and chrome.  You need to take everything off the frame and forks, and protect head-tube bearing races with wood bungs or take them out, optionally replacing them with new.

Since you've gone to all this work to clean the frame, may as well finish it properly too.   Fill any holes and sand and prime it, then paint with many thin layers of good paint, lightly sanding between layers and let it cure properly before the next coat.

Another option is a full-on powder coat paint job by a pro.  However the costs keep going up, so you need to weigh the value of the bike to you against the time and effort required.

I can't speak about chrome - never really had to deal with that side.  There are chrome spray paints in rattle-cans but they seem to be cosmetic only, and not shiny.