It depends on what the little round lamps are. If they are 230 volt then in the main the answer is yes. Where the problem arises is where the original lamps are 12 volt.
There was an advantage with 12 volt with tungsten quartz halogen lamps, it resulted in a thicker filament which would last longer and allowed the use of an electronic device which carefully controlled the energy given to the lamp as but under and over average voltage (Called RMS) would shorten the lamp live.
As a result the expensive heavy toroidal transformers were replaced with lighter cheaper switch mode power supplies which actually did a better job. These were called electronic transformers even though if the contained a transformer is was quite a small part of the whole device. The only disadvantage when introduced was the leads between transformer and lamp had to be kept short but because of interference and volt drop.
The electronic transformer has both a max and min output so with LED replacement this min value can be a problem. The tungsten lamp even if the power was pulsed still gave out a constant output, but any pulsing with the LED will be likely seen.
This means the old power supply is often unsuitable for the new LED lamps and can fail to work due to under current, and cause lamps to flicker, and can deliver spikes of voltage which can damage the LED and the latter my not be realised for 6 months after fitting and at the price of LED lamps finding they fail in 6 months rather than 10 years is not really what you want.
So with extra low voltage lamps (12 volt) one either needs to replace the power supply with a smooth DC type or move to low voltage (230 volt) instead, the latter needs an earth so often can't even use old wiring.
The forums are full of people having problems swapping 12 volt tungsten to LED best option is to go to 230 volt fittings.
The LED is a current dependent device and one needs a driver to convert from voltage to current these are normally built into the lamp. However some manufacturers call a DC power supply a driver so one has to be very careful matching lamp and power supply. Specially on the internet miss labelling seems common one has to carefully look at the volts and amps and see if they match.
In your case the replacement is likely wanting a 12 volt static DC supply and the 320 mA variable voltage supply will not do the job, the latter is a true driver but the one you want is also often called a driver.
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