Is it possible to carbonate in oak barrel?

I have 5L american oak barrel and I think I will try to carb my mead ale in the oak barrel by add the primming sugar for the carbonation.
Do you think the oak barrel can keep the CO2 inside the barrel?
I would like to try but not sure that the CO2 will escape or not, anyone has done this before?

I'm thinking it would be difficult to get a tight enough seal to prevent CO2 from leaking out.

They generally aren't made to hold that kind of pressure. That's why a winemaker will put an airlock on barrels when a nearby barrel is going through malolactic, just in case the culture kicks off in its neighbor. The resulting pressure in a stoppered barrel can be quite a mess.
C02 is commonly used to top off a barrel that cannot be topped off with wine, just to reduce oxidation, but not to create pressure, just displace the air.

the beer will naturally take about 1 volume of CO2 at room temperature without being pressurized. you can get about 1.7-1.8 volumes without pressurizing (<1psi) by chilling the keg down to near freezing. just be careful that you dont actually freeze it though, wood casks dont like frozen liquids inside. most likely you wont get anything more than 1-2 psi, if that.