Does spring of sophomore year gpa matter

To answer your question: your sophomore spring GPA is very important. 

From my recruiting experiences, only some of the EBs (EVR, PWP, MOE, PJT RSSG), satellite offices and a couple BBs (Citi and CS popularly) recruit during the Spring, or before mid-May when you would get your spring grades back to update your resume. 

Most recruit during the Summer or even during the fall, so you should be fine. The BBs like GS, MS, JPM, Bofa all start around mid-June to early July.

Barc, CVP, UBS, JEF, DB and some other groups don't recruit until September. 

You may be able to show it to some banks during the summer and fall. The above post is a general guide although I'd argue a lot of banks expect applications to be in by May, even if they don't get into full swing into June or July. Some years banks randomly go early, and COVID pushed a bunch back who would normally go by spring so who knows what they'll do now.

Also, you absolutely need to network before you apply, and you're going to have to use your current GPA for that.

Depending on how low your GPA is right now (3.0 vs 3.6 is a different story here) you could push your graduation back to December instead of June. This would give you a whole additional year to raise your GPA and recruit again as a "sophomore" next year. You can go through recruiting twice so don't worry about this now, but if you hit the end of the season with nothing it's an option.