If you are willing to move past the ugly feelings of shame and find a way to get past it than of course it makes you stronger. Going through a tough time in life and being able to keep your chin up and ignore those terrible thoughts and feelings will make you stronger.
Despite being shamed or going through some sort of shameful moment it is not the end of the world. Getting past this and reaching deep within oneself is courageous and brave. It brings up a new type of strength that person may have never realized they had. So, yes, you can gain strength from shame.
It is my opinion that a person can gain strength from shame. After experiencing a shameful moment it may be difficult at first, but learning to move on and reach past this obstacle helps that person find a new strength from within themself. It shows that person that they aren't easily overcome and have the ability to move on and take on harder tasks they may not usually try.
If the person you are shaming is yourself, then sometimes yes, it can make you stronger. However, it goes both ways, theres been a recent uprise of parents shaming their kids on social media to 'solve problems' or as a punishment, I think that kind of shaming is unnecessary humiliation. I also feel that weight loss shows such as the biggest loser who shame contestants who don't loose any weight as causing unnecessary humiliation, and i think it is horrible, and three quarters of the time the shame makes them feel worse about themselves, which for overweight people will cause even more problems.
I believe shame can wear you down, tear you up and spit you out. You can't hold your head up high anymore. It can go to the point where you don't want to leave you home. You don't want to face or talk to anyone. You become weak, and in some cases, suicidal. No, shame brings nothing but heartache.