In Illustrator should I check "Embed Colour Profile" box when saving a seamless pattern for print?

Wendy, I suggest ask your printer -

1: as D.Fosse mentioned - it's important to know which CMYK profile they use to characterise their press process

2: do they want an embedded profile in your file

Embedded icc profiles are very useful, because they tell a colour management aware application program about the provenance of the file. [How it was created].

So, if only for on-screen viewing an embedded profile can be rather useful.

There was a time when some antiquated plate-making RIP software would choke on a file with an embedded profile and it thus became common for printers to say no to embedded profiles. I hope those days are largely over. 

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

The question is which CMYK profile will be used for this. You need to establish this first. The Photoshop default profile (US Web Coated SWOP) is probably not be the right one here. If it isn't, expect colors to shift a little and you may need to readjust.

Embedding the profile is to make sure the file will be correctly treated downstream, further on in the process. It's not strictly necessary if the final printing process (and profile) is known with certainty, and all the numbers in the file are already in that final output color space.

CMYK is somewhat different from RGB in this respect, because you normally don't want CMYK to CMYK profile conversions. RGB is much more forgiving here, mainly because there is no K channel and eventual overprinting to consider. Embedding the profile means all future profile conversions will be correct.

In short, with CMYK, work with the correct profile from the start.

The pattern would be saved as a JPEG.