it will likely be fine for your trip alex, although it may not hold up for multiple years. a lot has to do with how well you take care of it (like anything). i've car-camped plenty in walmart-branded tents ($40- $60 stuff) in my life and have had no real problems. it also helped me appreciate the better quality of a more expensive tent once i acquired one. the more expensive ones tend to pack smaller and lighter, have better seams, better zippers, and MUCH better poles (stainless steel vs fiberglass which splinter and crack over time).
if i were you, since you have time, i would try sleeping in it in your yard on a rainy night to help gauge effectiveness. truth be told, you'll probably be just fine!
i'm excited for you that you've committed to making the big trip to spearfish!