In most cases, yes. You may need a 2.5" to 3.5" bracket to properly mount it in the hard drive cage, though. Nothing too big to worry about, there's no moving parts in an SSD, so if you have to, you can just plug it in and set it on the bottom of the case or somewhere out of the way.
Most cases have hard drive cages meant for 3.5" drives, so there should be no issue with your other drives, assuming they're 3.5".
I took a quick look at that case, and if you do indeed have to remove the hard drive cage to get your GPU to fit, you might want to send it back and get something else, because it looks like it's all one part.
I have this exact same case from Newegg
It says
Two front loaded HDD cages for up to 6 hard disk drives
Maximum Video Card Size: 16" (406mm) (Note: some video cards may require removal of the adjacent hard drive cage)
I'm assuming one can be removed, so it should fit in I guess?
Card size is
Card size L=312mm, W=129mm, H=43mm
15.9" x 9.3"
Also, my dad made a good point that I should probably just use the new HDD and SSD since the HDD actually takes power consumption and generates heat, and I will never fill in 2TB