Um, no, they can't. Blocking the game from connecting to the Internet is as simple as Zonealarm. And they can't bring any lawsuits against you if it's not illegal in your jurisdiction to download games (and, in many jurisdictions outside the US, it's not). Not only that, but the little fish are just too many and too insignificant to go after.
Not having broadband has nothing to do with this, as in any case, you wouldn't be able to download it, regardless of anti-copy. If the best argument you can think of for companies still using DRM is "well, they must have a reason, they can't be THAT stupid, right?", then I'll simply refer you to the reason behind it. As one of the fundamental characteristics of the universe, it's not something to be taken lightly.
As I said, only those with active consciences pay for games.
And, as for SecuROM not being "all that draconian", I guess I just have a very low tolerance for bull****.
Spoofing means creating false pirate downloads as well as posting messages that such and such torrent file, crack, application doesn't work, on the major file sharing networks. It is usually not very effective. It's got nothing to do with a game connecting to the internet. Anyway, taken together, fear of lawsuits, spoofs, and the sheer size of dvd disk images all have an effect on the availability of pirated games. If you can't download a game you would have to order one instead. You get me.
It's not a battle the companies are winning mind you, but if they gave up control completely they would lose more money. It's not like there is an alternative to trying to protect their work anyway, so inertia in relation to what.
The music industry is starting to make money off downloads because they finally understood that impulse buys have to be easy, and the price has to be good. Of course any kind of pay per download scheme would be impossible without DRM.