Generally speaking, no. Laptops are designed to be portable and secure. All of the components are locked down pretty tightly within the case and are designed in a way that they can work at all angles and tilts.
If anything, you may not want to move it too much while you have a disc in the optical drive, as it is possible to cause damage and scratching to the disc. But for the most part, these laptop optical drives are designed to work pretty well under most conditions.
That being said, never drop/throw/etc your laptop, as that can and will cause problems.
It’s also worth noting that if you are moving the machine more than a little, it is advisable to put the machine into ‘Standby’ or ‘Hibernate’ to ensure safety.
In most cases picking up a laptop and moving it around gently isn’t going to cause problems.
That said, you want to be careful when you have sharp shocks to the laptop, this is because if the hard drive is reading or writing information the head isn’t in the locked position. When there is a strong shock the head might hit the platter and cause physical damage. I would advise against going off roading with your laptop, sky diving, etc. Basically it’s not a huge issue but something to be aware of.