If a Linear Program (LP) has Totally Unimodular constraint matrix, integer RHS vector, and has an optimal solution, then it has an integer optimal solution.
But what about additional optimal solutions which are not integer? Do any mainstream LP solvers ever return a non-integer optimal solution on such a problem? If so, can/does this happen if solved by 1) Simplex, 2a) Interior-Point with crossover, or 2b) Interior-Point without crossover?
Bottom line: Are you chancing it if you need an integer solution, but submit the problem as a continuous LP?