Will this receiver drive my speakers, or should I get an amp?

Depends on your needs and your beliefs.

There is no simple calculation. I will say this, I doubt you can reach THX reference levels with the 861 without some clipping. Maybe not at all, I did not look at your speakers as links were dead.

However, you can probably listen at what I consider to be reasonable levels of 80 to 85 dB.

Some people believe amps are needed/are better. This is a self fulfilling prophecy. They believe they need an amp, they spend the money, and then when they put their amp in place they say 'Wow, I am blown away by adding this amp.'

I added a two channel Mackie to my system to check it out. I did not personally notice a significant difference. Maybe it was a bit louder.

If you want loud party level music, without blowing your speakers an amp might help as many people have reported blowing their speakers during parties. Alcohol and loud music seem to dull the senses and no one is paying attention to the fact that the sound is not as clean as it was at a lower volume level - a potential sign of clipping.

I would say don't crank it too much. First off the speakers your using for the fronts and center are 4Ohmn. These will demand more from you receiver than the rears which are 8ohmn. Also the receiver you are getting on the back states 400w consumption, yet 105wx7 output. Just doesn't add up to a receiver that will pack a punch.