Nope, no requirement to see Doctor Who prior to Torchwodod.
Personally speaking, the show is a bit irregular in it's quality and has numerous issues.
Season 1 could be subtitled "Men Rule, Women Drool" given the majority of the seasons treatment of women. It's so bad the show actually felt openly misogynistic without having to read too deeply into it. I'm still not sure if that came about purely by accident... but even then it seems a stretch to say all those coincidences didn't add up to some deep seated misogyny.
I mean come on, there were only 13 episodes and in them the only two times lesbian sexuality was brought up, they were both due to a woman possessed by an evil alien. Different women possessed by different aliens I might add.
The season arc is pretty much everything you'd expect from an RTD run show, in that it was utterly awful and totally nonsensical.
Season 1 felt like an immature view of what an adult show should be, with a focus on sex and swearing rather than adult characterisation and issues ("Cyberwoman" is perhaps the greatest example of what it's target audience truly was, or atleast the mental age of it's writers.)
Season 2 was an improvement, but that's not saying much. The characters however are now more likable, much better written and a lot of what occured to them in season 1 gets simply forgotten (which is for the better sad to say).
Season 3(the specials) was really excellent and I'd go as far as to say it's probably the best TV sci-fi around (though not something I'd want to watch for extended periods of time). A huge shock compared to the prior two seasons I can tell you. This is what Torchwood should have been and to be honest I wonder how much input RTD actually had in this.
Season 4 I haven't seen.
Overall the only reason I stuck with Torchwood was because of it's connection to Doctor Who. A real real shame since the concept itself was actually good.