No, reminders are per account. There have been some discussions in the past of people using email filters/rules or calendar setups to set up reminders for just those tasks you want.

This glaring omission is a frequent request. I hope very much the team turns their attention to it at some point. The best workaround suggested to far is to use smartlists to gather groups of tasks that you wish to be reminded of in similar ways, and then feed those smartlists into Gcal with different default reminder settings for each list. Roundabout I realize, but it does the trick very well.

Original idea not mine, and found here on 2/11:
https://www.rememberthemilk.com/forums/tips/4245/

Thanks for the suggestions. I'll check them but but I'd definitely like to see per-task reminders at some point!

+1 task-specific reminders.

We definitely shouldn't need to use workarounds to get this type of functionality. It could even be a Pro-only feature, but regardless this feature should be implemented.