Does it really make a difference for a second grader...
I'd agree with the others that it does matter even for a 2nd grader. Both of my girls had a lot of damage done in the early elementary years from classroom fits that didn't work well. We took dd11 out of first grade in the last quarter and homeschooled for a bit. She's a 7th grader now, has been back in school for some time, and has not had any lasting issues from 1st grade as far as I can tell.
Dd9 learned nothing in 1st grade and, with a different personality than her sister, didn't cause problems as a result but she came out with rather damaged self esteem when her achievement scores were no longer as high at the start of 2nd. She started to come back self image wise in 2nd and her achievement scores came back around only to have everything go downhill fast in 3rd. Her teacher was convinced she wasn't gifted and told her as much regularly. Anything she did well on was attributed to good guessing, which I still hear from dd - "I just guessed well." Being a compliant child, she isn't a problem in school, but she also isn't reaching her potential and she isn't feeling good about herself. We are trying to move toward hsing for her at this point as a result.
Having a good fit and learning something in school is important even early on IMO based upon our experiences.