I think I remember reading here that someone let the epoxy coat get tacky before laying a cloth on a paddle to help it to conform around the edge of the paddle.

I agree with Bill - It's almost impossible to get 'normal weights -3,4,5,6 oz -glass or carbon to wrap around a sharp edge.
Do the two sides separately, perhaps with a tape 'shelf' to support the glass/epoxy beyond the edge when you do the first side.
Some Greenland paddles have 'blunter' edges; you could probably wrap cloth around those with some attention and massaging as the epoxy sets up.

Can cloth be applied over tacky epoxy?

Yes, but it's difficult to deal with wrinkles, so I'd only try this on a small area. I think Nick (?) mentioned this as a technique for handling (very slippery) carbon fabric, but I may be 'mis-remembering'. :-)

And if so, could another coat of fresh epoxy be applied right away to better saturate the cloth?

Not just 'could be applied' but should be applied in my opinion. I want to get complete epoxy saturation into the cloth.

If you are looking for a clear finish, I would recommend using the 'tried and true' methods if possible.

For large areas like the hull or deck, I like to spread the cloth over a smooth dry surface, smoothing it out with a clean bench brush, then applying epoxy by pouring and spreading with a Bondo spreader. Then remove the excess epoxy as Ted Moores first described.

For laying up coamings and seats by hand, I add layers 'wet', though the first layers have usually started to harden by the time I'm finished.