Common to all jurisdictions (as far as I am aware of): It all depends on who commissions the drawing, and how. If the client makes you, the designer, or the firm that will come up with the drawing sign a work for hire clause, or any clause really that all works produced are owned by the commissioning party, then unfortunately you have no say over the published drawing's origins.
In any case, the designer of a drawing would probably have a really hard time arguing in court that they had the original idea for the drawing, since at that point the patent would be approved for a lawsuit to even be worth it.
Then I (as someone who has commissioned designers in the past), would argue that there is a moral argument against the designer seeking ownership over a client's patent. Technically, as a designer you are being asked to fulfill a role in the application process, unless you were part of the team or group that came up with the invention obviously. If the later isn't the case, then you are in a position where the best tool to fight a patent in court would be to seek a prior art argument.. which is inherently going against the service you provide as a designer since you would have to prove that what you actually put on paper was not original. This would imply that you did not do your own due diligence in drafting the patent drawings which, depending on who you face in court, could find you in hot waters.
Additionnaly, going through this route would also mean that you'd be undermining your professional credibility if you actually do find prior art to your OWN drawings. This creates a precedence around you that what you produce might not actually be original or performed in the interest of your client. So really, a form of career suicide..
Again, if this is something you absolutely want, then you should bring it up, especially if you actually end up bringing feedback or positive alterations to the original inventions. However, this is still tricky, since that final decision is at the discretion of your client, which can very well walk out the door to another designer who wont ask this of them.
To balance out my point though: you could always, if dealing with a startup for example and if you have authority to make this kind of arrangement, ask for small equity in your client's project/company if they can't afford paying your for perpetual licensing royalties; ask for name recognition somewhere or work references etc. You can be creative, as long as your client is too and agrees to put it in writing (very important).