Probably possible, but not the way I did things. I used 16 color palettes for most of the graphics (excluding the art gallery and Mission Matrix of course) and I didn't have enough colors to go around for the effect. I could have moved the shields to their own layer- I had one left after the border, background, and font- but I was having considerable trouble finding a free character block and screen block about halfway through the design process, and just gave up on it. There probably is a spare character and screen block lying around somewhere (a game like GORF doesn't make heavy demands of the GBA hardware), but the way Dragon BASIC uses tiles makes it tougher to hunt down and use them than it probably should be.
It's really not too hard to pull off this effect, if you've got the room for it. Just create a graphic speckled with different colors, then change those colors with rapid palette swaps. I was able to do this with the ship's last explosion, since it's a sprite and I find those to be a lot more versatile and accommodating than tiles.