No spark wiould not be caused by the timing belt, as you say. If you have to work with that dealer, I'd insist on talking to their best mechanic, and not the idiot you talked to before. As for your 3.5, pull the 98 FSM I have as it will be the 3.5 SOHC that your 01 has. Shouldn't be too many differences for the engine itself.
I'd also have the battery tested. Just replaced mine after a couple of weeks of occasional and odd things like power loss, sudden stall (it's an AT), radio blinking out and losing memory settings. It tested with good amps, but well below the original rating, and was also 4.5 years old. Over a week with the new one and nothing odd so far. That is longer than I had gone recently up to that point. You just never know what a failing battery will do to you...