You cannot embed the ISRC code from Logic and if you're only going to sell digitally (iTunes etc) you provide the codes when you upload the songs by typing them into the relevent box when asked. It's exactly the same for other vendors like Bandcamp.
On CD's the ISRC codes are embedded in the TOC lead-in, where all the pq codes and CD text etc live (as per chorleymans answer above - sorry, was typing when you posted). AAC's can be tagged but anyone could remove or change the tag. There's no real way to embed them with the audio.
And do you really have to buy the ISRC codes in the U.S? In the UK we apply for free membership to the PPL where they assign us a unique code, and then we can assign our own ISRC codes as and when we need to. Look into it as I'd hate to see you, or anyone, needlesly ripped off.
ps - just reading on the US riaa website that there is a one off lifetime fee of $80 that will then let you assign your own ISRC's, up to 100000 per year. You may already know this - apologies if so.
http://www.usisrc.org/about/obtaining_code.html