The only thing I have experience using is tobacco (lots of it, unfortunately); and I have no reason to think it stops me from having, or recalling, dreams. All smoke is not equal.
Who dreams and/or recalls them is generally (substances aside) a matter of stages of sleep, when dreams occur. Another factor in the mix is whether someone "gets a good sleep" or not. Not everyone needs a lot of sleep, but some people (for one reason or another) can't get into a "good" enough sleep.
My personal "thing"/"theory sort of") is that people who have become addicted to tobacco tend to be people who use it as a way of "giving them what it takes" to be able to either deal with stress, get done things they need to get done, and generally process things (thoughts, stresses, emotions, etc.). The person who needs to keep functioning, regardless of whatever else is going on is, I think, more likely to be someone who (if they were foolish enough to do "social smoking" as a young person) finds himself a smoker who has trouble quitting. I don't think occasional tobacco would be "applicable" here.
Separate from any ways that medical marijuana may help some patients, I generally tend to think that people inclined to use that particular "smoke" are more "all about" "doping up the mind", or else at least dulling thinking and "getting away from it all".
In any case, I've never seen a difference in whether I have or recall dreams, whether that's from non-smoking days, occasional-smoking days, or days when some of the horror and stress I had to deal with not only wouldn't have allowed me to sleep, but wouldn't have allowed me to keep functioning and keep up with my responsibilities as someone who just didn't have the luxury of "zoning out" or heading for the couch and sleeping (or drinking or doping) my responsibilities and worries away.
Ironically, I suspect that during those times in my life when I most relied on tobacco "to keep going" facilitated my own clear sorting out/coping skills and allowed my sleep/dreams to remain peaceful and "as usual" as ever.
I imagine someone with experience using the "completely-other-kind-of-smoke" can provide insights on that. As for those who use/have used both types of smoke, I'm not sure sorting out "the dream question" would necessarily be very easy for many of them.