Yes 

That’s exactly what it means. So once all boats have rounded it, the mark can be moved to the new position. Rule 33 also allows the alternative of placing another mark in the new position while boats are still using the existing mark. Often preferred in shorter courses where time is tight. Usually a different colour and/or shape to avoid confusion, and must be stated in SI. 
Standing by for all the ‘yes, but what if’s’.😊

John A:
Yes, you can move the mark into it's new position after boats have started the leg.  What you have to do before the first boat starts that leg is to let them know it is being moved by displaying the Charlie flag and displaying +/-, the new heading, or a red square/green triangle.  The mark does not have to be in position until it is actually is in play for rounding or layline calls.  For some races, the mark may not even be visible because of the length of the leg, i.e. a 3nm windward leg, so does it matter that it is not actually set as long as the sailors know where it will be.  You do not have to have the first mark set at the start either.  If the course is to go to a windward mark 1 nm from the starting pin the signal boat can simply display the course axis.  This makes it easier on everyone.

You don't need to display the axis bearing.  Sailors know where 'windward is.

Other John A:
True, but in shifty conditions I would think it is good practice for the signal boat to display that if the mark is not visible because of distance or not being in position yet.  Without displaying it, you could have accusations that the one side of the course is being favored to favor a boat.  Better to say it up front and not have to justify it later.  But as you say, they do know what windward is.

A similar case I experienced concerns restoring a mark to its proper position even if boats have started on that leg. One mark in a leeward gate drifted several hundred meters out of position. The oncoming fleet was a mile away or more when we pulled the mark back into place, and some of the other support boats (not competitors) were concerned that we had violated a rule. As it happened the fleet arrived to find the gate restored and there were no complaints. I read the rule as limiting a change that must be signaled. The change must be signaled before boats are on the impacted leg, but a mark being restored to its correct position doesn't need to be signaled.

If the fleet is close enough to be setting up for a rounding, the better response is to fly the M flag and replace the mark with a boat, but on the occasion I'm describing the fleet was 10 or 15 minutes away. 

Jay, Repositioning or replacing a mark in accordance with RRS 34  is not changing a leg of the course as covered by RRS 33.

If you are using a penalty start flag, the triangle requires the first mark.

Mike re: "If you are using a penalty start flag, the triangle requires the first mark."

Very interesting insight Mike.

I might counter that the entire Appx J, rule 28 and sail the course require/rely-upon marks to be designated and their order and location to be known, but as we are discussing some rules allow the mark to not be in place at the start. 

So, I think that the location of the first mark will be known prior to the warning signal and thus satisfy the triangle requirement.

For a bit of fun, another angle: In an ‘out-and-back’ race where the only rounding mark is an island of diameter 1 mile which may be rounded either way - to port or to starboard - 5 miles from the starting/finishing line, the ‘triangle’ isn’t a triangle!