Yes, you can make image transformations for your webapp fast by piping in a C-extension, because the C code can control the i/o and data organization as well as the algorithms. The integration surface is tiny. You can't, however, make the language's memory usage and garbage collection faster. At least not as easily. You won't be "dropping into C" to fix your garbage collection problems, at least not in the way people dream of when they think of "performance problems" at the outset.
Whenever I see "I'll write in Ruby and optimize in C when I need to" I assume the context of "my program is well suited to be written in Ruby." For instance, I certainly wouldn't write embedded code in ruby. However, I would venture to say that these situations are the exception rather than the rule.
These days most software has access to fairly reasonable computational resources. If you're writting microcode for some industrial control system, or calculating stock price variations with micro-second resolution then certainly stick to C or ASM or what have you. However, in an age when even a fridge will have a few hundred MB of memory, and when a lot of code is meant to be just "good enough" I think even ruby will suffice.
Think of all the saved time ...
After profiling a backfill script which was looking like it was going to take about two weeks to run, I found an area where certain bit-twiddling was being done which was extremely slow in Ruby. I rewrote this section in C, and was able to make this section 1000x faster then the ruby equivalent (this was MRI 1.8.5 several years ago). The total runtime for the script was brought down to about 8 hours (from about 165 TPS to around 7,000 TPS).
Fortunately, I've found that Ruby makes it exceptionally easy to write C extensions, and I often think of reusing C libraries in cases where I'm worried about performance.