No. On the Canon EOS 350D/Rebel XT, there isn’t a practical way to disable the mechanical shutter and shoot time-lapse with a true electronic shutter.

For this camera, every frame uses the shutter mechanism, so a long time-lapse will add real shutter wear. That said, shutter life ratings are only estimates, and failure usually means replacing the shutter assembly—not losing the whole camera. The XT is commonly cited around a 50,000-shot rating, and many shutters last beyond their rated life.

If you specifically want a camera for lots of interval shooting, a compact Canon that supports CHDK can be a simpler option. CHDK can run intervalometer scripts and is often well suited to tripod-based time-lapse, especially when you don’t need DSLR advantages like interchangeable lenses, very shallow depth of field, or an optical viewfinder.

So: use the XT if you need DSLR image quality or lenses and accept the shutter wear, or consider a CHDK-capable point-and-shoot if ease of use and reduced mechanical wear matter more.