Hi Peter, this tool is rated to drive 14mm staples into wood, so yes both of these tasks are within the capability of the tool. However you may be better looking at our other model on Screwfix.com Screwfix code 53860 - our 0-TR250. It has an adjustable power selector that will allow you to set the depth the staples drive. Important when firing through thin material as you described. Also it fires 12mm and 15mm nails, which might be better for tacking ply.
5 sizes of Stanley Staples available on Screwfix.com
1-TRA704T 9087c 6MM/1/4" H/D STAPLES(1,000) G TYPE
1-TRA705T 84461 8MM/5/16" H/D STAPLES(1,000) G TYPE
1-TRA706T 88872 10MM/3/8" H/D STAPLES(1000) G TYPE
1-TRA708T 67749 12MM/1/2" H/D STAPLES(1,000) G TYPE
1-TRA709T 5795f 14MM/9/16"H/D STAPLES(1,000) G TYPE
We hope you enjoy using your new staple gun.