There’s a lot to this question, so I’ll have to break it down into multiple parts.
Yes and no.
There is no tool for automatically synchronizing an LFO modulator to an autopitch modulator. However, the effect of autopitch is very similar to applying a linear pitch automation curve to pitch, so you could potentially automate a property of an LFO modulator and design a similar curve.
No.
To be honest, I’m not sure I understand how the LFO modulator would help achieve this goal - but more importantly, attempting to make our example engine sound like a specific vehicle engine using only effects and modulators is a fool’d errand. No amount of filtering an effects will produce a result more true-to-life than an actual recording of the car in question.
As I said above, I don’t understand what property you intend to attach the LFO modulator to, which makes it hard for me to definitively answer this question. I can say, however, that if you attach it to an event property, you would be able to do it without having to apply the modulator to every individual instrument in the event; whereas if you attached it to an instrument property, you would have to repeat the action for ever instrument in the event that you want to be affected.