That should solve some problems for you then - the upgrade I mean. For what it's worth I have v7.31 and am very happy with it. Though I use ID CS3 solely at work I have Quark at home and use it fairly regularly. v7 is miles better, in my opinion, than v6.
However, yes, there are some small issues you'll need to be aware of between v7 and v6. Firstly try not to work on legacy files. If you need to open a v6 document in v7 it's recommended you start a new v7 project and thumbnail drag the pages in from the v6 original, then work on the new, fresh, v7 file. Otherwise you can experience some slow downs and oddities.
Next up downsaving - generally no problem, though of course you lose any v7 specific stuff. But you do need to make sure the copy of Quark 6 is patched up to 6.52 as there were issues with downsaved files and earlier versions of v6.
Lastly, and obviously, just be careful! Downsaving anything, in any program, should be treated with care and double or even treble checked to make sure nothing weird has happened.
Good luck,
Greg