I suspect that a prior knowledge of Russian would actually be quite useful for studying Georgian. I'm currently working my way through chapter 15 (the last chapter) in Aronson's Reading Grammar, so I'm almost done, and the book does have a lot of references to Russian particles and functions that apparently have no English equivalents. I particularly had a lot of trouble with chapter 14 for this exact reason: e.g., he compares the suffix -ღაც(ა) to the Russian suffix -то and the suffix -მე to Russian -нибудъ, and I'm still not really sure what the difference is between the two suffixes. I think I've figured it out, kinda, but it seems it would be easier for a Russian-speaker.
There are also some other similarities. E.g., I know that prefixed Russian verbs form their future conjugation with the same person markers that the corresponding non-prefixed verbs use to form their present conjugation, e.g., Читает vs. Про-читает, and Georgian uses a similar system for forming the present and future conjugations of class I and II verbs, e.g., წერს vs. და-წერს.
I've never studied Russian though, so maybe this is the full extent of the similarities. Well, this and the many loan words and calques, etc.