Well, it's a bit more complicated...
First of all, nothing is going to blow up or be damaged. There is no harm using higher-speed memory than a system calls for.
But the mHz speed rating of memory, these days (probably for the last 10 years...) is just a convenient marketing term. The actual specification consists of a number of different ratings (perhaps a half-dozen or so) for various aspects of a memory access cycle. This is too complicated to explain to consumers, so manufacturers tag a mHz rating on it.
Pick 10 different "pc2700" modules from different manufacturers, and they are likely to each have a slightly different set of specifications. That's why there are "premium" brands or lines within a manufacturer. The most common differene in premium memory is a small number of cycles for "CAS latency".
A small ROM on the memory module is read by the BIOS, and is read to determine the specifications. The BIOS then sets-up the chip set to optimally match those specifications.
A higher-speed memory than required for a given system CAN, to some degree, offer some memory speed improvement. This may require manually setting one or more memory parameters in your BIOS setup.
For example, if you use a higher-speed memory than is required, you can often change the CAS value, say, from 3 to 2, even though the memory is rated for CAS 3. The thing is, it's rated for CAS 3 at a higher speed than you are running it at, so it can be safely run at CAS 2 at a lower clock rate.
The converse is not necessarily true. A "premium" brand of memory that is rated CAS 2 will not necessarily run at a higher speed than it's mHz specification by derating it to CAS 3.
Of course, it's all a black art, since there are a half-dozen or so different specifications to juggle, and many of them interact. Gamer sites engage on endless discussion of this subject...