Absolutely, If it's your one and only strop, you need it virgin, no paste, for daily use. Pastes are for minor honing.
You have your Chromium Oxides, TI, and Diamond Pastes, and the Dovo's. For minor touch up, like your blade starts dragging on your skin, You might try the Chromium, or Cro2. Diamond pastes are also popular, you have .025, .5 and 1.0
Most guys use the .5 and the .25, but some complain that it leaves their face irritated, so cro2 seems to be the most popular. So, basically, You need a seperate strop for pastes, maybe multiple if you plan on using different pastes. I recommend Tony Miller highly. He has nice wide paddle strops for pastes. (The Well Shaved Gentleman, Heirloom Razor Strop Company, Straight Razor Shaving Supplier) Most guys on here will tell you the same. He's a real nice guy. His wood components are Amish made, which is cool. Hope this helps,
Rich