No, not recommended since it desolves during every wash and rinse cycle instead of just the last rinse cycle. Besides wasting product, it also runs counter to its intent - it hurts washing performance if you add rinse agent to it. Kind of like adding conditioner to your shampoo, or liquid fabric softener to your laundry detergent. The soap/detergent is doing its best to clean off the Jet Dry et al.

I don't think rinse aid and detergent would work against each other. After all, both contain surfactants and there are some detergents with rinse aid (substitute) available. These rely on an extra-heavy dose of surfactants that are supposed to last through the interim rinse(s) until the final rinse.

Here's an current discussion on JD:

Alex

Here is a link that might be useful: JetDry Solid - 4 Washes and it's almost gone!