Can I log time in a Cri-Cri twin-engine aircraft?
What a positively delightful looking aircraft!

I see no reason you couldn't log time in this as multi-engine time - it clearly has two engines, with two separate sets of controls (at least throttles, from what I can see).

Similarly I see no reason you couldn't fly it IFR as an experimental aircraft, provided it's "properly equipped" (consult the FARs for all the details on what you need), passes an IFR pitot/static test, and has appropriate radios (Transponder which you'd likely need anyway, Com, and Nav).
Whether you'd want to take it up in real weather is another matter though :-) 

For that matter if you want GPS you could certainly have it without much weight penalty: throw in a Garmin GNS 430W and cover the Nav/Com and GPS in one ~7-8lb box.  Whether or not that kind of investment in what's basically a single-seat super-ultralight is "worth it" is a judgment call only you could make, but it definitely seems possible.