Yes. Adding dyes to RNA was common practice for Northern blots in the 0ld days

In terms of where you add your visualisation dies, there are various options:

1. Into the agarose

2. In to the buffer

3. In to the buffer plus agarose

4. Neither but post stain gel at the end with buffer +gel red

5. Or as you have suggested (common for RNA)

However, I am wondering why you would add it to the sample and not the buffer and/or agarose ?

One detail I would add to Laurence's answer is that adding dye to the gel,buffer or sample will make the sample run about 10%slowere compared with running the gel and then post staining but post staining is much less convenient

GelRed works by intercalating with the DNA in your sample and will fluoresce when exposed to UV light. If you add the dye straight to the sample the when the GelRed binds to the DNA and like Paul says when you run it on a gel it will run slower due to the addition of the extra molecules bound to the DNA. 

It is much more common to add the dye to the agarose or to post stain as you really need a very small volume of GelRed to visualise DNA.