Yes, it is doable. It is A LOT of sanding. The better you can get the brush marks to flow out, the less sanding you will have to do.
It's not the best choice, but you can thin with acetone. MEK (Methyl Ethyl Keytone) also works as a thinner for polyester resin and gel coat. Don't confuse MEKP (hardener) and MEK.
FiberGlast has the following to say about thinning with acetone: "While acetone is an effective solvent, we strongly recommend that it not be used to thin resin or gel coat, as this can lead to added pinholes or premature yellowing."
Polyester resin and gel coat is styrene based. The technically correct thinner is styrene thinner.
http://www.fibreglast.com/product/Styrene_Thinner_70/Polyester_ResinsIf you need to add wax to non-waxed gel coat or resins:
http://www.fibreglast.com/product/Styrene_Wax_71/Polyester_Resins