Yes. Most of those gaps can be fixed by unscrewing the screws, clamping, then screwing back into the same screw holes.
Green (wet) "2 by" material will usually take a screw without splitting like that, which is why they sell it for construction (it will also warp as it dries). If you are using kiln dried or green that has dried out you should really drill pilot holes. A pilot hole through the first piece of wood about the diameter of the screw you are using will keep the screw from biting into the first piece of wood which will allow you to pull the 2 pieces of wood together without a clamp. Selecting a screw with an appropriate unthreaded section will allow you to do the same thing, pull the pieces together. The unthreaded section of the screw keeps the thread from biting into the first piece of wood.
I always glue and screw my stands for extra strength. Some times I will only screw parts of a stand without glue for the specific purpose of disassembling the stand at a later date so it can be moved.
I know clamps can get expensive but you really would be much better off getting some pipe clamps. Pipe clams from Harbor Freight work fine and are pretty cheap, it is the pipe that can get costly. Lowes and HD have always cut pipes for me for free but charge for threading the pipe. A 10' pipe cut in half will give you 2 x 5' pipes with a single threaded end for a pretty reasonable price. I prefer galvanized pipe but many save a couple bucks by buying black pipe instead.