Those few that have tried it have not reported any significant side effects from interchanging ABS and non-ABS ECUs and cars. However, several of them had already disabled the ABS systems.
The engine ECU does control the ABS on the DSM cars. It is not known for certain if a non-ABS ECU has the ABS circuitry installed at all. As in the case with knock sensor circuitry, different ECU models (in that case, turbo and non-turbo) might be the same ECU without certain parts.
In theory, an ABS ECU should work on a non-ABS car just fine. However, there is a strong possibility that the ABS ECU might "see" the lack of ABS equipment and cause the ABS light to turn on, because the ECU tests the ABS system on each startup.
Also in theory, a non-ABS ECU should work on an ABS car. In this case the ABS system might not work since the ECU may not have the circuitry necessary to operate it. If it did work, warning lights indicating an ABS malfunction might not work as intended.
As always, YMMV. There are few examples of DSMers trying this swap.