. . . . whether the app deals with interlacing correctly . . . .
The simple answer is yes, however you do need to be aware that the final video depends on what format you are exporting to - not all formats support interlaced video - they are progressive only.
If you export to a format supporting Interlaced - you will get 2 fields - one Top (odd) and one Bottom (even) per frame.
If you export in a progressive format eg MP4 h.264 then both fields will be combined to create a progressive frame.
The progressive export from interlaced video can cause issues with combing on across the screen fast moving objects, this is inherent in converting Interlaced video to progressive, as there is a time difference between the fields during which the moving object has moved.
. . . . . does this mean that I should export to a non-progressive format for the clearest picture . . . .
Assuming the source/captured video is interlaced - then neither are 'clearer' then the other - it all depends on the media and/or playback device the video is going to be played on:
DVD or Blu-Ray disc, then it should remain interlaced. This will be taken care of automatically if you use Rescue your Video Tapes to create a disc.
TV from memory stick or external hard drive - best would be interlaced (AVCHD) however, if the TV will not play back AVCHD, then you may be forced back to progressive eg MP4 h.264
Youtube/Vimeo etc, then you have no option but to export progressive eg MP4 h.264. Computer monitors are progressive devices.
Note: if you are capturing from VHS tapes then the quality/clarity is going to be 'poor' - VHS has an approximate resolution of 335 x 576 (PAL) or 333 x 480 (NTSC) ie both are lower quality then standard DVD (720 x 576 or 720 x 480).