I do not believe that there is any restriction on how you climb, there is a max of 1500 f/m within 1000 of your assigned level.
Also the A/P must not only have an alt hold function but also a warning that the selected alt has been deviated from.
Prob means can climb/descend manually but not cruise.
You can not normally remain in RVSM space if the A/P decides to take a long term break from proceedings.