I guess it's a matter of whether the OP just wants to mount it on the acrylic with the printed face out (not recommended, unless it's reverse printed, or laminated on at least the face to protect it), or whether he's looking to face mount it, as shown in the link provided. If the former, and the possibility of some shadowing and/or color shift isn't a concern, the light coat of spray glue might be okay. But, if you are going to be looking at the print through the adhesive, it's not a route I think I would attempt to take.
The actual arcade machine marquees are screen printed in reverse on the substrate. Conversions were often a Duratrans which were simply taped at the edges to the inside. So if one is looking for that authentic look, a layer of acrylic on the front, regardless of the method used to get it there, is what one would be shooting for.