Infants are born with irregular sleep cycles that take about six months to mature. Ideally, it would be best to put him in his crib for naps and bedtime that's your eventual goal anyway. But for right now, if he will fall asleep in the swing (often that swinging motion is calming and helps babies fall asleep), that's okay.
Babies often look uncomfortable all curled up with their neck bent over in the swing, but this position does not seem to harm them. Keep in mind that he won't fit in the swing for very long, so if it works for now, use it.