Nobody is going to know exactly what these connections are doing, except maybe Postbox since they wrote the app. I usually search around, find what I can, and make a decision. One can always deny and see what happens. If everything works, that connection wasn't needed.
All three of the websites you listed are the same IP address, which I found by the method in this thread viewtopic.php?f=1&t=7623 The address is also google-analytics, youtube, and others.
A web search leads me eventually to this page https://developers.google.com/safe-browsing/
It sounds like maybe Postbox is checking URLs in email messages for security, as you suggested, but probably also enabling Google's data mining operations.
All three of the websites you listed are the same IP address, which I found by the method in this thread viewtopic.php?f=1&t=7623 The address is also google-analytics, youtube, and others.
A web search leads me eventually to this page https://developers.google.com/safe-browsing/
Safe Browsing is a service provided by Google that enables applications to check URLs against Google's constantly updated lists of suspected phishing and malware pages.
It sounds like maybe Postbox is checking URLs in email messages for security, as you suggested, but probably also enabling Google's data mining operations.