I assume the doors are flat, with no moulding. Yes, you can use a roller. You will not like the finish however. Rollers have a nap which leaves a very fine texture. ITs great for walls but not doors.
Why is a brush "dreaded"? My guess is you have always used cheap brushes. There is no substitute for a quality brush. Get a 3" brush ($10-15) and a plastic bucket.
A quality brush will hold more paint and show fewer brush marks. This makes for a faster, neater, smoother job.
Do not dip the brush into the can (it ruins the bristles). Pour the paint into the bucket. Dip just the tips (about an inch) into the paint. Then tap the walls of the bucket, do not use the rim, to knock off excess paint. Paint with the tips of the brush.