*schnipp schnapp*

It's an issue of what Bitcoin Core will use. If it's statically linking an OK version of OpenSSL, then updated your system OpenSSL is OK. If it's dynamically linking, then you'll have problems. The binaries on bitcoin.org statically link OpenSSL. I think that almost all Linux distros distribute versions of bitcoind/bitcoin-qt that dynamically link.

If you're compiling Bitcoin Core using the normal configure+make, then it'll link dynamically. I'm not sure how to force this to link statically.