It's doable, but probably won't be as easy as you'd hoped.
Discogs has an API so you can send a query in the form of a URI and you get back xml formatted text. You would then need to parse this to extract the data you want. From the looks of it you first need to search for the catalog number then extract the title from the hopefully single return and submit that to get the disc information you want.
I'd think that you'd need some plugins to make life easier when submitting the requests and getting back the data without using webviewers. I've used Scriptmaster from 360works to do something similar.
You'd need to parse the text, either by importing it via an XSLT stylesheet after writing it to a file (better when there are multiple records in the xml file), or running text functions on it and setting the fields with a script. Here a regex plugin might be easier than most of FileMakers built in text functions. (Regex Plugin -- http://jensteich.de/regex-plugin/ or Text Toolkit -- http://www.dracoventions.com/ both are free and distributable)
The questions you need to ask yourself are these; is solving the automation puzzle less work than copy and paste manually from a webviewer set to automatically generate a search based on the catalog number? or if you are not adding to the data why not just view the data online, is there a need to have it locally?
I think I agree, It will most likley be better to cut and paste from a web viewer, I will try that.