Unfortunately there is no way to turn off the shutter mechanism on the 350D (without some serious hacking, which would probably render it useless as a DSLR).
A DSLR is probably overkill for timelapses and not really simply the right tool for starting to learn how to shoot them, mainly due to the mechanical shutter. But also the major advantages of a DSLR:
- interchangable lenses
- shallow depth of field
- optical viewfinder
are not usually required for timelapses, except in rare circumstances. At the same time the disadvantages of P&S and bridge cameras:
- poor low light performance
- slow autofocus
are largely mitigated by shooting timelapses on a tripod. Other advantages are that a smaller camera is easier to position, you can get away with a lighter tripod or a GorillaPod. It's also less likely to get stolen, and if it does it will be cheaper to replace. You don't need the latest and greatest, HD video is only equivalent to two megapixels! You don't even need manual controls or an intervalometer if you can a camera for which a custom firmware is available (e.g. it supports CHDK).
Is this the only timelapse you'll ever shoot? Or will you be planning to do more if it goes well? If it's the later my advice would be to stump up the cost of a compact now and it'll save you money in the long run.
The manufacturer's shutter ratings are conservative, and empirical data on shutter failure (such as this link that Joey posted for the) is very useful, but beware of the small sample size! There are a total of 10 people (out of 427 respondents) who claim to have taken the camera past 150k actuations. The 427 figure is also not representative considering the millions of 350Ds that have been sold worldwide.