No, there should be no break...
I have multiple domains, not even "sub-domain" in some cases... In my case, we have our main site (i.e. www.domain.com) and our subscription site that is shared for the majority of our sites (i.e. purchases.org.com)
I have entries with campaigns to www.domain.com, and I can see those campaigns apply to the Orders that occur on purchases.org.com
I am not using WebSDK, but that shouldn't make a differences... the values should be stored against the user / session.
However, there may be things that are breaking the session? For instance, have you ensured that both domains are listed as "internal urls" in your report suite configuration... also, this one is going to sound weird, but I had issues in the past if I also didn't code those into the "never track" for the automatic exit link tracking... even though the suite was configured to have both as internal, if the actual tracking triggered an exit click to another internal domain the pathing / session info seemed to get weird... so I always make sure to configure in both places.... this also helps with efficiencies (to not track an extra server call when moving between domains). I assume WebSDK has a similar exit tracking configuration...
Check if that might be causing an issue?