If the Tamron has a Canon mount, than YES.
What is your reasoning? It is not at the same quality level as your 5D Mk II? I believe it is important to keep your equipment balanced. It is possible it will not focus properly so if it is a used copy, you may want to try it out before you lay your money down. Plastic build.
From the reviews here
It's a decent lens that is EF mount but it also seems to be hit or miss on getting a good copy. Without knowing your intended use & how fussy you are about your images it may fit your needs but then again it could be the weak link in IQ.
A 21MP 5D Mark II will be a lot less forgiving of any lens weaknesses, than your 8MP 30D was. But I see no reason not to try it and see if it gives you satisfactory results. The Tamron 19-35mm appears to be a "full frame" compatible design, so give an adequately large image circle to be able to work on either FF or crop cameras.
Some older third party lenses (i.e. Tamron, Sigma, Tokina) will not focus or stop down properly with later Canon cameras, even though they might mount just fine. The problem is usually the circuitry or firmware of the lens is incompatible. The reason this happens is that Canon lens-to-camera technology is proprietary. Rather than license it from Canon (if Canon even would issue a license, I dunno), third party manufacturers reverse engineer lenses to work with current camera models. That might be fine for the time being. But if Canon makes a change in later camera models, the lens might no longer be compatible. Since that Tamron lens worked fine on your 30D, it certainly will fit on your 5DII, and there's no concern about the lens giving adequately large image circle since it's designed for FF, but there's no guarantee it will focus or stop down properly.
In all cases I've ever seen where there was an issue, it simply causes an error on the camera. You can then remove the lens, turn off the camera and remove the main battery for a few seconds, reinstall the battery, turn on the camera and all is well... No harm done. Except you now know the lens is incompatible with the camera. There might be a very small risk of "bricking" a camera... essentially damaging the circuitry or blowing a fuse. But you'll usually find lots of reports of that happening online (for example, there have been some reports of the 31mm macro extension tube in certain sets "bricking" Canon 5D, but this is pretty well documented online). I don't see any reports of that particular Tamron doing any harm.
If it were me, I'd give it a try. It will likely work... or you'll quickly know it won't.
I have an older Sigma 24-70mm lens that functions fine on my EOS film cameras and DSLRs up to 30D, but won't work on anything later than that. In certain cases you can send the lens to the manufacturer to get it updated to work. In the case of the Sigma I have, it's just not worth it.... I think I only paid $7 for it used! It's unlikely Sigma would even have a means of updating it.