The short answer would be no.
In Sir Charles's case, from what I can gather, he never received all three and certainly not all at the same time. He may never have received the gratuity and he resigned the stipend when he received his pension for wounds [whether on his own or under the regulations, I do not know].
There are many gaps in this area, but from what I can gather, being 3,000 miles from the sources [8^}:
By at least 1775 officers were entitled to a gratuity of one year's pay for loss of limb(s) or being maimed. This was reaffirmed in 1798. I have no idea of what constituted being maimed then. However, evidence indicates that the list of eligible wounds expanded between 1798 and 1812, again no idea of the types that were now eligible or what they were worth.
Later, it was decide that the army would go to a pension system similar to that already in place in the Royal Navy issued in a Royal Warrant in 1812. The pensions were made retroactive to 1793. I have not seen this Royal Warrant of 1812 to know what it covered and exempted, just some excerpts. The pensions were apparently graded as to rank and type of injury and officers could receive more than one wound pension if they received eligible wounds.
Unless there was a stated length of time to receive the pension, I imagine he received it until death?