The answer is NO. Absolutely NOT! And here's why:
1. they will think you have no idea what you want - you want a career, that's clear, but you have no idea what to choose; you want to try it all out before you decide. This is not OK. The company needs someone reliable with clear decision making skills.
2. they will think that you have no idea what each job is all about - you can't possibly like all jobs and want to do all of them; this means that you haven't bothered to find details about each one before applying;
3. you want to be promoted at any cost and want more money - that's it - you don't really care about the job or the company;
4. you desperately want out of your team or you want a new manager; they will start asking what is wrong with your current team and manager;
5. you have no decision making skills - you can't decide what you want.
Did I convince you? I hope so.
Applying to too many open positions may "help you" lose them all, including to that one you may have been perfect for.
Take care,
Geo
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