It might help to just download 15.2 and try it with your exact version of Java, to be very sure. Even if it is with an empty database and just a sample pipeline. I doubt that 14.4 supports Java 1.8, because they removed some of the ciphers Go was using in 7u85 (look for "Prohibit RC4 cipher suites" in
this document).
Because they've removed it in 7u85, and you're going from 1.6 to 1.8, I don't see a way without upgrading everything together. If you leave it at 14.4 and upgrade to JRE 1.8, then the agents won't connect since the ciphers are gone. If you upgrade to 15.2, leaving the JRE at 1.6, then 15.2 won't work as it needs 1.7.
What you can try, if it makes sense for you, is to upgrade the server to 7u79 (not 7u85 or above). 14.4 should continue to work - especially agents. You can check that, and if not, revert to 1.6. Now, you can upgrade the server to 15.2 (since you're on JRE 7). Agents should all upgrade themselves and continue to work. Now, agents can be upgraded all the way to 1.8, in a phased manner, if you want. Both 1.6 and 1.8 agents should work.
As Jyoti said, we haven't tested 1.8 agents with 1.7 server. So, no real guarantees about JRE 8, unfortunately. I'd test this with a fresh install of 15.2, to see if it works. I'd definitely wait for Jyoti to take a look at this and respond (probably Thursday, since she's away for a day). She probably knows this best.