To get back to the original question, I think arming raw civilians with either bows or crossbows would be of marginal effectiveness at best given the state of the world in most T2K campaigns.
I'm assuming that the players still have automatic weapons as do many of their adversaries. I find it doubtful that an untrained group with homemade crossbows will bring much to the party. The likelihood of doing much damage is low as is the likelihood that they will be able to stand and fight effectively. Remember, low morale and unit cohesion usually come with low training. They might actually be better off standing off with higher quality weapons. They'll probably stay in the fight longer.
Two other thoughts though. I'm not saying that a highly trained professional couldn't make useful tactical use of these weapons. An elite soldier with a crossbow is probably a better bet than a novice with an AK in close quarters. Also, these weapons should become more and more effective as technology recedes. Bowmen couldn't stand up to even primitive firearms and I don't expect they'd do very well against M249s either, but when these weapons wear out they will once again have a lot to offer. It's just that most T2K campaigns still have a higher tech level than the one at which this would be an effective strategy.
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