Yes, most likely this data will conflict. There were significant changes in trophy files format from 0.1 to 0.2, which will probably result in your trophies being not detected - the 0.1 daemon will definitely not see the trophies generated by 0.2. I am not sure, but it is very probable that it will also be the case if you try to open 0.1 trophies with a 0.2 viewer/daemon. Considering that, you may end up in some trouble.
However, if you really want to use such setup, it is possible to use separate directories for your trophy files for each of these systems - just tune the
~/.config/accomplishments/.accomplishments file. 0.2 is now released, so 0.1 is outdated anyway, thus you may prefer to just upgrade your laptops's Accomplishments to 0.2.
We hope to stabilize the trophies format, and hopefully future versions will not suffer because of such conflicts.
In general, this depends on the application. Some applications rely on the format of data they synchronize using U1, others not. In case the data format is not significant (e.g. the application shares photos and music), conflicts are unlikely - if the format is significant however, it would be best to use the same version on application on all synchronized devices, especially if the application is overcoming major changes from version to version.