Certainly. Neither having but one jib, as Malabar II has, not having a marconi main makes a boat not a schooner.
You might get more of an argument about what Capt Pete Culler called his periauger schooner scow which had no headsails but just fore and main. But that's just a distinction to define the type of schooner, just as one might distinguish a staysail schooner from other types.
You can even add more clutter is you think the LFH Marco Polo is something other than a schooner, with three masts fore, main and mizzen, each with triangular sail, and as designed a knockabout bow and simple jib.
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