In this case (April 4th, 2015) you could safely click "Connect". But in general such warnings should not be ignored. Here's how you can investigate future occurrences of such warnings:
Clicking "Show Certificate" and then selecting "Google Internet Authority G2" showed for this incident:
Google Internet Authority G2
Intermediate certificate authority
Expired: Saturday 4 April 2015 17:15:55 Central European Summer Time
This certificate has expired
And for "smtp.gmail.com":
smtp.gmail.com
Issued by: Google Internet Authority G2
Expires: Thursday 31 December 2015 1:00:00 Central European Standard Time
This certificate has an invalid issuer
![](../../I/static/images/53dd47410c8ea571efd55700b5305767c286a00b0f553bd7266797eae6a3e59f.png)
So, the certificate for Gmail was still good, but the "intermediate issuer" that was used to create it didn't last as long as Gmail's certificate. That was an error at Google's; meanwhile they have installed a new certificate on smtp.gmail.com which uses a different issuer certificate. However, as this was trusted until a few hours before the problem started in April 2015 (and assuming you used it before, when all was good), it was safe to select "Connect" then.
3
This is not the first time either: https://www.seroundtable.com/archives/017825.html
– Antoine Jaussoin – 2015-04-04T18:43:08.8831
And by now should be fixed: https://www.google.com/appsstatus#hl=en&v=issue&sid=1&iid=bf1b188b6295f21fbfc92d7b48dfe7be
– Arjan – 2015-04-04T20:52:37.523