(Please note: this question is one of many "why don't you just try it?" questions. I certainly will, but since I haven't found an obvious answer by googling, I thought I might as well make it easier for someone who might need this later by asking on ServerFault)
My web application is served over HTTPS behind some load balancers and allows users to authenticate using client certificates in some cases. Now I'm being asked whether I'd like to offload SSL encryption/decryption to load balancers so that I'd be running a plain HTTP site (and thus with easier debugging and configuration) while the load balancer would be doing HTTPS for the users. Free extra CPU cycles certainly sound good, however, I'm not convinced that I'd still be able to check users' client certificates.
Is it possible to use client certificates without running a full-blown HTTPS site?