Short answer is NO.
Ive owned 20+ car's so far and I never got those feelings.
I wish I still had my 67 Camaro w/ ZZ4 and a stalled TH400 that my ex ended up getting in the break up, but a little part inside of me is glad it moved on and I dont have to deal or think about it's small problems anymore. I miss it about as much as my first car which was a root beer brown 74 Maverick with the Grabber package.
Here's my first GM muscle car that I bought when I was 18. Pic was taken a few years later when I was 21 at my then new house. Notice the brand new for the time, 275/60/15 BFG comp TA Drag Radial