Can a 2005 jaguar s type go into (and out of) limp mode without storing a code?

 

Probably.

E.g. if someone cleared the codes / OBD status and it was unable to figure what code to flag due to having unset OBD monitors.

(A very good reason never to clear codes without being sure you know what you're doing. And battery disconnect is another trap.)

A failing battery might also be a cause. I'm sure there are more, all fairly rare - though commoner with somewhat neglected cars.

It's also possible to have codes but an OBD tool that fails to report them - not all tools work properly.