I will be the first to admit that I'm in love with my Titanium status. I don't know for use it "opens doors" for me when it comes to upgrades, but I will say this though. As a frequent visitor to a few hotels, I'm greeted by name, sometimes before I arrive via email letting me know that I've been upgraded. And when I've applied SWA, my upgrades tend to be for the higher end suite selected. There have been a few times that my SWA was returned but I still received upgrades to nice suites.
If Titanium is "within striking distance", I will make it a point to "go for it". But in the end, I have enjoyed being Plat as well as Titanium knowing that the room selected is the type I want and any upgrade is well appreciated...