Yes it does. You just have to be a bit careful about how you do it.
The reason lots of people don't like simple resistors is that they are running either in vehicles or off batteries. Both of those experience a significant range of voltages. Coupled with a resistor and some LEDs, that equals a HUGE change in current, which is the last thing you want in an LED.
Since you have a fixed voltage, you have much less of a problem. You do still have to deal with the fact that from one LED to the next, they are a little unpredictable. Say you are going to buy some Cree XR-E emitters, and plan to run them at 1A. You don't know if the forward voltage will be 3.4V, 3.3V, or 3.1V. So you can't determine in advance the exact resistor to get you exactly 1A. Also, the forward voltage drops a bit as they heat up. In marginal designs, this can lead to a situation called thermal runaway, where the LEDs heat up, the forward voltage drops, which causes the current to increase, which causes more heat, which causes more voltage drop, and around and around until something fails (usually the LED). The way to cause thermal runaway is to have the supply voltage close to the LED voltage, and use a small resistor, and have poor heatsinking on your LEDs. The way to avoid it is to use a larger resistor value, and a higher supply voltage (or lower LED voltage). Unfortunately, this reduces the overall efficiency of the system. Good heatsinking helps too, but is also a tradeoff.
But you can plan on starting at a safe point, and gradually decrease the resistance until you get the current you want. Or, if your power supplies have a voltage adjustment (many 'fixed' voltage supplies have a small trim range), start at a low voltage and turn it up to where you want.
Say your supply can adjust from 11 to 13V, and your LEDs are somewhere between 3.0 and 3.4V at 1A, at operating temperature. You MIGHT be able to run 4 LEDs in a string, but you'd have to be careful of thermal runaway. Much safer to run 3 in a string, starting at 11V and 2 ohms. That would give you 1A if the LEDs are at 3.0V, but you probably will have less than 1A. Now you can measure the LED voltages, and get a better idea of the right resistor value.
By the way, measure current by measuring the voltage across the resistor, not by measuring current directly with the meter. The meter has enough resistance to change the current in the circuit.
But say you wanted to run 9 LEDs. Your supply can put out 5A, and each string is only 1A, so you can run 5 strings. I would use separate resistors on each string. If you buy all the LEDs in the same batch, it's safe to use the same resistor value on each string. If they are different LEDs or are from different batches, I would test each string individually.