No they do not. My main CPU (s) gets interrupted by my drivers nonstop. As networking or disk goes up, my apps slow down even if they don't depend on them since the CPU is absorbing the hit of many of those operations. That's totally different than a Channel I/O-like model where a dedicate CPU manages all that with apps just handing it off asynchronously in a high-level way, I/O processor doing low-level stuff, & scheduler making sure nothing slows down due to waiting on it. That's why my CPU is sometimes under 10% utilization when it could be working big time but mainframes are more like 90-97%.
Or maybe you meant they have specialized hardware... dedicated ASIC blocks... to accelerate TCP/IP processing, compression, filesystems, database operations, and so on? I didn't see those for decades either outside custom cards or chips on the motherboard. Definitely not in SOC's designed for them with smooth CPU integration. That's come online recently under semi-custom banner at AMD/Intel & all these Cavium-style processors that merge CPU's + HW accelerators.
So, there's a difference between what highly-efficient, I/O model some products have right now and what my desktop computer has. The servers are catching up with all kinds of fast buses and add-on cards. Need changes at CPU and OS levels, though, for max effect.