Red Tank Light And Plants

Plants photosynthesize using the red and blue light of the spectrum (they reflect the green, hence they look green). So it will be 'of some use' to the plants. However; there are far too many variables in your question to even start to say how good it would be.

Just for fun, have a skim down this to get an idea of how complex the subject of photosynthetic radiation is.

EDIT: Not to mention that it may make your tank look like a brothel.

I'm assuming this is actually one of those lights with a pinkish glow rather than a true "red" light. If so, it probably won't make much difference to the plants either way. However, I find that a full white light makes the fish look better, under the reddish light some colours can look dull.