No, this game has no co-op mode on the PC. It's way inferior to the previous SC games in general and actually can't even be completed without using various workarounds, due to the horrendous number of bugs. If you want to buy it, I would strongly recommend getting it on the consoles instead, especially the Xbox1/PS2 version. Unlike the 360/PC version, it was made by the same dev team as Chaos Theory and is apparently a completely different and much better game (and has a co-op mini-campaign like CT).
Does CT's co-op work for you? I've wanted to try that out for a long time, but I remember people back then saying that the co-op in the PC version was totally unplayable due to lag and low framerates. I don't know if one of the patches fixed those issues though.