First of all, change of an email address does not impact your access to Intuit Link. It does, however, impact email communication you may receive from Intuit Link (e.g. daily activity reports and account recovery) and, of course, security if you no longer own that email address.
Are your email addresses under a custom domain? If they are and provided you have everything correctly set up (DNS, MX, etc.), your team's ability to receive communication from Intuit Link should not be affected. If you have problem receiving emails from Intuit Link, you probably then have problem with your email communication to/from others too.
If you're not on a custom domain, that will entail an update of your Intuit accounts with your new email addresses and that shouldn't affect just Intuit Link but all Intuit products, including PS.
I may not fully understand the context but if you could elaborate a bit more, I or someone else may be able to offer some suggestions.
Still an AllStar