Certainly — if you can have a Tactical Exercise Without Troops (TEWT) then you can have a Board Wargame Without Board And Hexes (BWWBAH).
The wonderful old game “Seastrike” worked like this, and I have just managed to secure (at vast expense) a copy of the Ariel second edition. Since my copy of AH’s “Afrika Korps” went walkabout many years ago, this means that at the moment, and until I acquire another game, the first and last games in my collection are both “Seastrike”.
I recall in the late 70s a bunch of carboard-cutout games published by Tabletop Games (not to be confused with Table Top Games Inc) that were very popular at our school wargames club. I hated them all, but not because of their cardboardiness.
At university, wanting a slightly more upmarket battlebox than other officer cadets in Exeter UOTC, I made myself a set of big Fablon-covered counters representing the elements of a rifle platoon (three gun groups, three rifle groups, 2-inch mortar team, MAW team, platoon sergeant and balloon banana) together with some anarchist militia and Fantasian enemy for them. Later I did a second set for a company each side, with heavy weapons, MFCs and FOOs, and, originally for purposes of free-time rehearsals of platoon attack ideas, whipped up an absurdly simple set of rules (“Foxhounds”, after the fixed callsign for infantry at the time) based on 1d6 and a couple of simple spotting and shooting tables and the assumption that what it said in the Sandhurst precis was a true picture of how minor tactics worked.
When I got my first edition of DBA — still, I maintain, a work of bowel-shattering genius — it didn’t take me long to work out some counter symbology along the lines of SPI’s PRESTAGS series for the different troop types (with the added wrinkle that, by counting the number of icons on a piece, some of which were shaded and some not, you could tell the basic fighting strength against foot or mounted without consulting the rules). Inspection of the army lists told me how many of each I would need to make to be able to field any legal combo of armies permitted by the rules, and I made up the counters, again Fablon-covered. As the period covered by the rules was before the days of NATO standard symbology, I coloured the sides purple and gold, instead of red and blue. The whole lot, in ziploc bags, with a couple of movement/shooting rulers, some terrain shapes and a set of the rules, fitted in a cigar-box. This accompanied me to Saudi Arabia, and in the six months I spent living in hotels before I could move into a compound and import more wargames (getting “Arab Israeli Wars” past the Ministry of Information man at baggage inspection was a triumph of mine) my little portable DBA set did a lot to keep me sane.
My COW games over past years have often used carboard counters — “Neverwar” on area maps, “Churchill Troop Commander” on a tabletop with terrain shapes, and “The Moon-Grey Sea” used stand-up ship counters on a square grid.
This junk is still knocking about somewhere upstairs or in my office, the “Foxhounds” counters still stored in old Rothman’s 20s packets from back in the days when they were allowed to mark them “By Royal Appointment”.
All the best,