The batteries will recharge, but probably too quickly, which would damage or destroy them. A proper charger will limit current going into the batteries to less than 1 x the "C rate" for a fast charge (1 hour charge), which in your case would be 2000mA. The batteries would stay healthier if charged more slowly, say 400mA (5-hour charge) or 200mA (10-hour charge). This is to say nothing of how you determine when to stop charging, which is complicated for NiMH and can be difficult to do right even with a chip making the decision.
A battery's voltage varies widely, depending on how full it is, whether and how fast it's being charged or discharged, its temperature, age, previous usage, and so on. NiMH is fully discharged at around 0.9-1.0V per cell and probably won't go much higher than 1.6V per cell during charging, but in between those voltages you can't tell a lot about the state of charge from voltage alone. You can't tell when to end charging by looking at a voltmeter.
If you know the batteries are dead and just want to get some charge into them, not a full charge, you could in desperation (or as a hobbyist experiment) connect the AC adapter set to 5V to the batteries through a 10 ohm 1 Watt resistor, which would limit current to approx. I=V/R or I=(5.0-2.0V)/10ohm or 0.3A for a roughly 7-hour charge rate, while also allowing voltage at the battery to float. The current into the battery wouldn't be constant, but it would be limited, which is what really matters.
You'd want to disconnect the charger from the batteries before they get overcharged, and since the only meaningful measurement you've got is time, you'd want to stop charging after 6-7 hours, maybe much sooner, depending on how worried you are about destroying the batteries. A 7-hour charge is for fully discharged batteries. If you have no idea how full the batteries are then you'd want to shorten the charge time so there's less risk of overcharging and ruining them. For a first test you might try only charging them for 1 hour and see how much runtime you get.
Such an experiment is unwise if you don't care about electronics and just want some charged batteries in the house. It'd be faster and safer get a new charger at the nearest drugstore, hardware store, or electronics store, as they're readily available for $10-20.