Based on my humble experiance. Tinning stranded wire is a good practice. The most important keys to success are to use the proper flux and no acid core solder.
Tinning helps reduce corrosion on the Cu and gives a more solid crimp connection.
It only takes a few seconds to tin. Repairing/finding a bad connection is very time consuming. I see this as a pay me now or pay me more later type of situation.