If the pivot point is in line with the center to center distance between sprockets then you won't need a tensioner as the chain slack will be minimum for our needs (+/- 2", 4" total travel This can all be calculated will simple trig functions.
Here is a quick xl spreadsheet calculation for chain slack for a rear suspension design where the pivot point is in line with the center to center distance between sprockets. It does not take into account sprocket sizes so may be slightly off, but not by much.
if you want to know how much it moves per two inch (approx) when it's not in line (fraction of an inch out) subtract the 4" from the 2" which is about .05". Compare to the .016" for the 2" movement here.
So yes, if your pivot is not in line you will need a tensioner. If it IS in line, you could get away without using one.