True ^ truth serum type stuff are disinhibiting substances like some barbs.. on DXM you are far more likely to just get robotic movement and maybe have more trouble speaking intelligibly.
There's always a chance, like xorkoth indicates, because if it's something that on some level you really want to talk about, then the intoxication necessary to undermine your self-control are relatively lower since you have an urge to tell... but no, DXM is not particularly the kind of drug that would cause it.
(Also, it varies a lot between people whether you are sensitive to losing control over your behavior - but usually you would learn that about yourself for example by having been drunk etc)