Yes, that is a very good idea. There are a number of sites that I have used that don't do this, and the result can be very frustrating.
Lets say that I have spent time looking at many items and I am many items below the search / filter component.
I would strongly suggest that you use what you have proposed. I only wish that more sites would do the same.
One alternative is to have the facet filters horizontally across the top and contract / expand them. Have them stick to the top of the page, or under other fixed items and you have a killer combination.
Also one thing worth thinking about with infinite scrolls is if you know how many items you have you can also give some indication of where the user is in the scroll (as technically it's not infinite - just long and has not pagination).
Let me know if you need more clarification on this.