Possible but not attractive if the time frames between upgrades was a bit longer.
Bought an Athlon X2 with DDR2 RAM in 2007.
Wanted an upgrade in 2011 and found that the price per GByte of DDR2 RAM was much higher than for DDR3 RAM. CPU and GPU needed changing anyway. 4GByte of DDR3 RAM were not more expensive than buying another 2GByte of DDR2 RAM would have cost. Some Athlons and Phenoms for socket AM2+ were still available but the socket AM3 CPUs looked considerably better.
So I settled on a Phenom II X4 on a relatively inexpensive new socket AM3 Board. Bottom line, I paid some extra for the new board but got better memory bandwidth and a more power efficient CPU out of it. The old board remained operational, as I did not rip out CPU, GPU or RAM.
I also still had a nice case from 2004 hanging around so I shelled out a bit additional money for a PSU and a new hard disk, and put the new system into the old case. Overall, I paid maybe 150 euros more than with maximum reuse of the old stuff. But that way I kept the 2007 PC usable, which is still useful from time to time :-)