Could this be a substitute for the bitter truth pimento dram in a navy grog?

Short answer - sort of yes, the end product will taste a little different and you will have to adjust up your sugar/simple syrup to compensate and produce the right balance. It might take some trial and error to get the right ratios. Longer answer - the "Pimento" in both cases refers to Allspice (this name is still used for Allspice in Jamaica and much of the Caribbean; "Pimento" means pepper, and allspice "berries" (actually seeds) look much like peppercorns (which are also seeds)). The Pimento Dram is an herbal liquor, and while the primary flavor is the same, there may be additional ingredients (it appears rum is generally the liquor base for Pimento Dram) as well as sugar (in this case, often brown sugar, which will further alter the flavor profile). The Pimento bitters may have other ingredients included, and will be subtracting sweetness instead of adding to it. You will need to increase the sugar component, and might want to use light brown or even dark brown sugar instead of white or demerara sugar to add back some of that depth and richness (unless you want a lighter body and flavor profile, of course). The specific grog recipe you're using may interact with all of this because of the other ingredients present, of course. The original grog recipe had only three ingredients - rum, lime and sugar.