I think the answer is "maybe" and the only way to find out is try some of the better heart rate monitors (Polar is one of them).
The electrical signal from your atrial fibrillation is generally smaller than the one from your two ventricles (responsible for most of the heart's pumping) because the muscle mass of the two atria is much less than that of the two ventricles. The magnitude of the electrical signal from the ventricles contracting, called the QRS complex, varies depending upon where the electrodes measuring it are located. This is one reason they use twelve leads for a standard electrocadiogram. Heart rate monitors only use two electrodes. You should try wearing the heart monitor's electrode strap in different locations to see if you find a location with satisfactory readings.
This seems to be the experience of users with atrial fibrillation. At this LINK they state:
However, there are a very small number of cases in cardiac rehabilitation
where the heart rate monitor will not work, for example: low voltage R-wave
signals, atrial fibrillation or bundle branch blocks. In your case we would
recommend to check the operation of heart rate monitor during ECG
measurement at rest and during exercise. Polar has developed the
transmitters to detect a normal ECG and the issues you described (on
earlier UK records) may have have an effect on your ECG. Thus, cause the
transmitter not to detect the heart rate.
Should it be that the transmitter cannot detect the heart rate being in the
"normal" position (on the chest), where the signal is normally the
greatest, it could be possible that signal of your heart is greater
somewhere else. Could you try to move it around e.g. wear it on your back,
on your stomache, on your sides?
Thus as another poster suggests, if possible borrow one or more models, try wearing them in different positions, and see if you get satisfactory results. I suspect the better, more expensive models may have low and high pass frequency filters and perhaps even auto gain adjustment that may let them detect the larger QRS signal and ignore the smaller fibrillation signals.
Do let us know how this works out for you. Best of luck.