Should be fine with that mesh for the under base yeah. As long as you can get a really smooth finish on the white, that's presuming you're flashing it then overprinting the white with the blue? I use Photoshop to do all our seps and halftone any gradients, process jobs etc. Never used Corel, so can't give any advice with artwork prep.
Best to expose with a single point light source to avoid undercutting.
You need minimal off contact for halftones.
A really good sharp hard squeegee.
Really straight well tensioned screens.
Try to use a light fast stroke with the halftone screen.
Go for it!
Post a pic up so I can see how it went man.