Not necessarily. It depends upon your own preferences.
Most professional removal companies will be perfectly happy to provide full packing services. In reality, many would prefer to be allowed to do so because it means they will know that the items have been packed to the highest standards ready for transport.
Even in that scenario though, it may be necessary for your own employees to assist in things such as the labelling of boxes.
If you wish, you can see to all packing yourself, though typically the removals company will attend to the physical loading of their vehicle, as this is a skilled job and may also be a requirement of their insurance cover.
Note also that if you ask your employees to engage in packing and lifting as part of a removal activity, you may be putting elements of your own employer’s liability cover at risk, as such work could not be construed as being part of their normal daily legitimate duties.