I've just tested out this using Teamcity 8.0.2 and subversion 1.8.3. They're working together without any issue.
Both server side and agent side checkout work, however, if you're planning to use any new 1.8 based features (agent-side checkouts) that requires a client that is minimum 1.8 in version, you have a problem, since teamcity uses a java library for svn operations (svnkit), and the latest bundled lib supports 1.7 and lower working copy versions.
See this feature matrix: http://subversion.apache.org/docs/release-notes/1.8.html
If you don't need 'working copy record moves', 'automatic reintegration merge' or any other feature where the minimum client is 1.8, you're good to go.