In short: No, it will not run a 64-bit OS.
However, it will be a minimum of 5-7 years before 32-bit support may be completely gone from any distro - even from Ubuntu, which has given the shortest timeline. Even then, there will be smaller, more niche-oriented distros that will continue to support the 32-bit OS & libraries. I wouldn't be surprised if Mint takes one of those for an Upstream provider for their 32-bit offering. Mint already offers a Debian(directly) derived version, and Debian has not committed, or commented, that 32-bit is out.
Also, it bears mentioning that the whole "killing 32-bit" thing is a proposal from a Ubuntu developer, and a comment about the cost of it from OpenSUSE. No road-maps have been updated, no proposals accepted, or even formally submitted. This is the beginning of the conversation about if i686 should be discontinued.