I am no expert, but I asked the same question to the Sig people at the SHOT Show back in January and they said you could do it with one of the caliber exchange kits.
I looked at the caliber exchange kits and did not see anything different than a standard Sig slide and barrel. Maybe it was a Sig sales guy and they were full of shit or am I missing something, too?
I ran into a friend today that is a Sig armorer for a local LE agency and he mentioned he just did some refresher training a few months ago. He said that the current training includes the .22s and that Sig specifically says you can convert it to a centerfire caliber with the centerfire kits or (SIG SAUER X-CHANGE Kit™ in Sig’s marketing language). He said they showed it with the P226 .22 and a .40 slide kit.
I asked him if standard slides work and he said he didn’t know, but Sig said to only use the centerfire conversion kits with the .22s. Maybe there is something with the sig kits versus standard slides and locking inserts.