Highly unlikely.
In many years of research, I've found few authentic examples of men above conscript age (50 years old, law of Feb 16, 1864) who actually served in the Confederate army. Militia, yes - that's a different animal. But not in the Confederate army.

Plus, your source makes him a Mississippi soldier in Federal uniform. Assuming he's not a slave, this is highly unusual as well. The only Lee is Federal service from Mississippi is William H Lee, 1st Battalion, Mississippi (U S) Mounted Rifles.

Anytime a family researcher indicates that a man served in a military command, the claim should be examined very carefully. Too many people find a "likely" name match in an index, make a connection and never give it a second thought. Others see it and assume there is factual support for the claim, and the original error reproduces on the internet like a virus.

Don't be a family tree virus carrier!