Probably not. Rainbows need bright sunlight and Titan's atmosphere is dense and smoggy. The methane rainshowers are probably like a miserable, damp pea-souper.

If a tree falls in the forest, and no one's around to hear it, does it make  a sound? No - it makes a shockwave; sound requires there to be something which can hear it.

You would only get a rainbow if there was something there to see it positioned in the right place, and as stated above me, the sunlight isn't as ambient as it is on earth. Probably not.

 It's at least mentioned on this NASA page...

"A methane rainbow would be larger than a water rainbow," notes Cowley, "with a primary radius of at least 49o for methane vs 42.5o for water. This is because the index of refraction of liquid methane (1.29) differs from that of water (1.33)." The order of colors, however, would be the same: blue on the inside and red on the outside, with an overall hint of orange caused by Titan's orange sky

http://science.nasa.gov/headlines/y2005/25feb_titan2.htm