Is the processor in Lenovo Chromebook C330's any good?

Yes. Good

Although the Lenovo Chromebook C330 receives good reviews, I do notice its processor as a smartphone processor MediaTek™ MTK 8173C Processor (1.70GHz).
To estimate its performance, we need to see a table that combines all Mobile processors, and not just laptop ones.

Although testing is not reported, it estimates at rank #729, where lower number rank is stronger.
Apple tablet and smartphone 737 Apple A8 and 725 Apple A8X October 2014 iPads.
The Lenovo CPU is stronger than Atom x5-Z8350 @ 1.44GHz used on other cheap 11.6 inch laptops and tablets.
It is somewhat stronger than a Celeron N4000 and somewhat less than a Celeron N4100 or Pentium N4200.

This review calls it the best cheap Chromebook in the price range

It is designed for Internet use only, like a Netbook rather than a standalone laptop.
It is a tablet cpu.

The Mediatek 8173C reduces speed to 2100MHz from 2400MHz in the 8173.
The graphics processor is extremely basic PowerVR GX6250 in the range of Intel HD of a few years ago.

If you think of it as a versatile netbook, tablet and keyboard instead of a laptop, it does well for what it is. Don't confuse it with a standard laptop costing more money.

Depends what you would use it for, compared to the budget you have for it. With no clues about that, all that can be said is that it would be okay for Internet uses, like others tell.