Answer:
Definitely not. The neutral wires must be put on the neutral buss and that is the only place that they are to be terminated in a distribution panel. In a distribution panel there is no ground buss, it is just the metal enclosure that is used. The ground wire is only used to return a system fault back to the distribution panel to trip that circuits breaker.
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Distribution panels typically have two "busses"-- one for ground and one for neutral. These are terminal strips where the ground and neutral wires are connected. In some panels, these busses are electrically connected or "bonded." In other panels they are isolated. Most panels come with an optional "bonding screw" that can be installed or removed depending on whether the busses need to be connected. NEC is very specific on when these busses are to be connected. Ground and neutral busses should only be bonded at the main panel where the service enters the building. Other distribution panels will have separate ground and neutral busses and they should be isolated electrically--connecting these is a commonly seen mistake.
I believe the question refers to the case where the two busses are properly bonded together, so are electrically equivalent. Then is it acceptable to have some ground wires on the neutral bus and vice-versa. Electrically it will work, but code or electrical inspectors may deem it to be confusing or sloppy practice and reject the installation.
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As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.