Chips absolutely do wear out. Dopants electromigrate and higher temperatures make it faster. Discrete components like capacitors also tend to fail over time.
Is it going to be that significant though? No idea.
It's not normally an issue, but the edge cases can be very sharp. Otherwise, the bigger concern is the hardware becoming obsolete because of new generations being significantly more power efficient. Over a few years, the power+cooling+location bill of a high end CPU running at 90% utilization can cost more than the CPU itself.
Honestly it depends on a whole lot. If they are running 'very' hot, yea they burn out faster. If they have lots of cooling and heating cycles, yea, they wear out faster.
But with that said machines that run at a pretty constant thermal load within range of their capacitors can run a very long time.
Is it going to be that significant though? No idea.