No,no,no. On the Aerad/Thales charts there is a comment to the effect 'DO NOT CLIMB ABOVE CLEARED ALTITUDE DUE TO INTERACTION WITH OTHER TRAFFIC'. This means do NOT climb above cleared altitude until cleared so to do by ATC.
That's not what it says in the AIP, and I suggest that you review the chart you've seen very carefully, because your instruction leads to a very different answer from what I read into the intention of the AIP.
"WARNING - STEPPED CLIMB
Due to interaction with other routes pilots must ensure strict compliance with the specified climb profile unless otherwise cleared by ATC."
That makes it even more important that MAX ALT's question is resolved. The note suggests that it's dangerous to be
below the specified profile level. So if instructed to "climb to altitude 4000 ft", what do I do if it appears that I need to climb further to adhere to the profile?