Condoms, used correctly and with spermicide, are quite effective at preventing the spread of HIV. According to the CDC, "studies examining sexually active people at high risk for contracting HIV have found that 'even with repeated sexual contact, 98-100% of those people who used latex condoms correctly and consistently did not become infected'" (
link). Condoms used correctly and consistently are highly effective at preventing HIV transmission, even for people at high risk of infection (such as those with partners who have HIV).
And, of course, you can avoid exposure to HIV almost entirely by not having sex with anyone you aren't completely sure isn't HIV-negative (assuming you aren't engaging in other risk behaviors like needle-sharing, of course). I would personally suggest that if anyone is worried enough about HIV infection that they'd advocate government-sponsored tattooing of those infected, they should probably refrain from having sex with anyone they aren't 100% sure is HIV-negative, which means making sure they are tested immediately, and then again in three months (and then again three months after that if you are going to be REALLY certain), and being absolutely sure the relationship is monogamous.
Again, I fail to see how the tattoo would really help anyone. The only thing I can imagine it doing is stopping some people from having sex with someone who was HIV positive and would have lied to them about it. However, considering that many people would probably think that No Tattoo = No HIV = Woo Hoo, No Need For a Condom!, any positive health benefits would be greatly outweighed by the negative ones. There would be no way of knowing whether someone without the tattoo was HIV negative or HIV positive, but it is very likely that people would use their tattoo-less status to convince others they didn't have HIV, even if that wasn't the case or they weren't sure, or that people would simply assume that someone without the tattoo was HIV negative.
I don't see why it would change people's behavior. If you are being responsible, you are either going to use condoms consistently and correctly, or you are going to not have sex with anyone you aren't sure is HIV negative. And, if you are irresponsible enough to not do that now, chances are you aren't going to be responsible enough to examine your partner for a tattoo.