Welcome to Vector Linux!
Yes, Vector Linux Light will work just fine on your old ThinkPad. I have it running on a Toshiba Libretto SS1010 with a 233MHz processor and 64MB or RAM. Just don't expect to run any multimedia applications with it. gslapt, the graphical package manager, will be painfully slow. Using slapt-get at the command line will work very well. Opera may also be slow. The included lightweight browsers, hv3 and Dillo, will be faster.
There are several ways you can install without a CD-ROM drive. Which method is easiest depends on whether you are running Windows, DOS, or another Linux distro. They are all well documented in the iso but if you have questions folks here will be happy to answer them for you.