The reason why he tried to escape was due to the fact that she didn't know it was him because she couldn't see him anymore. In Chapter 64, Linn states that because of the destruction of the sacred grounds (Church of Alexander Mark/Tiger's Den for Butlers) people would eventually be able not to see him (including Hayate). Which is confirmed in Chapter 360 with Hinagiku having lost her ability to see Linn.
Could also be a continuity error since i think that Nagi also failed to see him at times. Anothier weird thing is that Sakuya seems to be able to see Father Linn (as seen in one of the chapters where Hayate took Maria to a date) even though she never enter the church
I'm certain the time various from person to person, but in Nagi's case she couldn't see him because she had lost the ability to after Church of Alexander Mark/Tiger's Den for Butlers was destroyed. As for Sakuya, perhaps she has the ability to see super natural things (ghosts,demons etc....) seeing that she's always accompanied Isumi when ever she performed any exorcisms in the series.
The real reason why Linn run is because he is scared that hinagiku can kill him(note:he is dead already) ^_^
Either way, I'm certain if she knew it was him. Linn still would have suffered from her wrath for being noisy (laughing at a gag manga) late at night.