estuckey,
Unfortunately not in the way you hope from what I can see.
If you ran a sequence for an particular object for 5 frames and you have your file name Keys set up correctly then the images will be numbered 0001 to 0005.
If you then ran the sequence again for another 5 frames, instead of these new ones being named as 0006 to 0010 they will instead be names 0001-1 to 0005-1.
Run yet again and you'll get 0001-2 to 0005-2
etc etc etc
While a sequence is 'In Progress' you can change the figure you have set in the current events 'Repeat' box which will automatically continue the original numeric sequence of the images as they are saved. But once the sequence has finished your screwed.
SGP is obviously intelligent enough to notice the fact you have already got 'Some' images for a particular object in the 'Light' folder so it would be nice to have an option in the 'Tools -> Options -> Sequence Settings' box which would allow us to instruct SGP to continue sequential numbering should this be the users desire, disabled by default of course, this has caught me out a few times in the past and can be really annoying I have to say.
Paul