If you are using Tridion 2013 SP1, that implies that the CD libraries are used in-process and hence the version of Spring is dictated by CD (or at least: the version of Spring you use should be 100% compatible with the version used by CD) and CD 2013 SP1 uses Spring 3.1.
Indeed, early DXA Java releases used Spring 3.2.8, but that has been found problematic and hence DXA Java 1.3 was downgraded to Spring 3.1.4.
So: the official answer is "no, because you will get compatibility issues with CD libraries".
If you upgrade to SDL Web 8 (CIS/CIL) this CD compatibility problem disappears (CIL doesn't use Spring), but the DXA Framework still uses Spring 3.1.4 (mainly because we also still support 2013 SP1).
In DXA 2.0 (in development) we have finally upgraded to Spring 4.3. This did require some changes in DXA because of incompatibilities in Spring.
Regarding configuration: note that "DXA Java 1.1" release does not exist; the first official DXA Java release was 1.2. Earlier versions were not official releases. Regardless, the way how DXA Java is configured has changed significant in early releases. I would strongly recommend to upgrade to a recent, official version. Since you're on 2013 SP1, DXA 1.6 is the most current release you can use.