He's only a good investment in two cases...1. He saves you from elimination.2. He nets you points in the final 250 that exceed the points you would have netted elsewhere.If Stafford isn't playing in the final three weeks and you just have Tannehill, you're not winning.
Some might have said that last year about Cam Newton. I once won a fantasy championship based on Kyle Boller's play in weeks 15-16 (540 yards, 6 TDs). When you have no idea how well a cheap player might be playing when it comes down to the wire, you can't predict whether he'll be valuable or not. At $4, it seems like a reasonable investment; you could have downgraded from Julio Jones to someone performing better, and had a better team.