No, not all and they could be damaged if you do.
Many legacy electromechnical attitude gyroscopic instruments include a caging device to hold the gimbals in place and 'force' the gyro gimbals to return to their home position. This instantly erects or resets the unit by pulling the caging knob. Some caged gyros include a cage lock mechanism, some do not. Some people believe that a cage-able gyro should always be in the locked position when handling, transportation, or storage takes place. This is not always the case.
For example, L3, manufacturers of the legacy AIM gyro product line, specifically indicate in their installation manuals and service letters that "instruments without cage locking mechanisms are designed to be shipped in an uncaged condition...using external locking devices to cage the indicator may result in damaging the caging system...". Southeast Aerospace has seen many people use external means to force a cage lock such as a spacer wedged between the extended shaft and knob. As indicated by L3 (AIM), this could very well damage the unit since you are forcing it to do something it might not have been made to do.
Most, if not all, gyro manufactures have detailed instructions within their installation and operation manuals that indicate how a specific model instrument should be handled, transported, and stored. This includes instructions on whether or not to cage lock the instrument or not. Always follow the manufacturer's instructions.
(Cage-able but does not have cage lock locking mechanism)
(Cage-able but has cage lock)