Due to my work schedule I'm pretty much limited to installing the tile in my basement one week during my off days and won't be able to lay the grout until the following week during my off days. Since the tile is in the basement, no one will be walking on it and I was wondering if this would be acceptable to allow this much time in between laying out the grout.

You should have not problem delaying the grouting. Be aware that any traffic risk breaking the bond between a tile and the sub floor until the grouting is done.

No problem. I have grouted tile that was laid 1 year earlier. Make sure to strike and vacuum the joints before grouting. It is best to do all the grouting at one time.

I'm using a grout additive to permanently seal the grout as I'm doing it and because I figured it would take me a good part of the day, I would have to wait another week to get it done. Thanks for the advice!