I tested 2015 SP1 (V1R6.1) on Wine 1.7.38 on Xubuntu 14.04.2 x86_64 and submitted the test results to the AppDB.  I didn't test any 3D commands but basic 2D operations work with a few problems.

It will crash with a page fault immediately after submitting registration info when activating the license.  To work around this, install Windows Management Instrumentation (WMI) with Winetricks (winetricks -q wmi).  However, only the 32-bit version of WMI is available so this doesn't work for the 64-bit version.  It may be possible to obtain native 64-bit WMI DLLs from elsewhere and use them with overrides set via winecfg but I haven't tried that.

Printing and printout configuration is guaranteed to crash every time.  It appears to be a problem with winspool.

When a drawing is loaded, it may not be visible until the display is refreshed (zooming is enough).

It may develop a problem when started.  A loaded drawing may refuse to display, even after refresh.  In addition, the initial mouse clicks of a command (toolbar button or selection window) may be recognized but subsequent clicks are ignored.  I believe these problems can be caused by leftover processes from a previous crash.  Exit the app and terminate any other DraftSight or WinMgmt.exe processes with top, htop, or your desktop task manager.  Then launch DraftSight again.

Other behaviors like license registration info taking a dozen attempts to submit (no "check email" dialog displayed) and non-default toolbars not retaining their displayed/hidden status are the same as the native Linux version so no problems there ;)

The severe cursor lag and erratic zooming in drawings with large numbers of entities is not present or at least much less noticeable.  That might be a bug but I'll hold off reporting it for now. :D