Will my QUADs drive Spendor S100s?

The 100s are not easy to drive to tonally correct results. That said, I once drove them with a 30W DNM -- it was OK at reasonable listening levels. I do think bi-amping (mid+high/ bass) rather than tri-wiring is a good idea.
I assume there is no way you can try yr amps on the speakers before you buy?

I have driven the 100's (sp model) with a nait 3r with good results. As always the better the source the better the music meaning you do not really need to equate quantity with quality.

I currently use the S100's and formerly used the Quad's but not together. So long as you do not have a very large room or try to play very loud levels I see no reason why they would not work. Most of the time you are only using a few watts and the 303 was an exceptional amp for it's time. If you like the way it sounds on the Prelude then you should like the S100's even better, unless the room is too small for them. Biamping will improve the sound. Bare wire will do a better job than the jumpers Spendor provides.

Actually the S100 is by far more efficient than the prelude. I have the S100s and in the past 15 years I have driven them with many tube amps, starting with Marantz 8b (35 watt per channel) to Marantz 9, 70 watt per mono block.
The S100 are very efficient and up to now the best speaker I could find for tube amps. As long as you have 20 watts available, you are just fine.