No. You may be thinking of "Fallen Idol", in season six. In this episode, Radar is seriously wounded on his way to R&R in Seoul (which Hawkeye encourages him to do), and Hawkeye is unable to operate as he feels so guilt-ridden over causing Radar to be injured.
Season 7, Episode 3. "Lil"
It was made in the 1940s
Indian Scout
Wheelers and Dealers Season 10 Episode 6
From Amazon.com - Another episode that looms large in the show's legend is the Emmy-winning "Dear Sigmund," in which weary and depressed psychiatrist Sidney Friedman sought refuge at the 4077th. This episode further fleshed out BJ, and established him as the camp's practical joker. FriPilot
Beej
Good Bye Spelled out in rocks so Hawk could see it from the chopper as it lifted off.
This was the episode entitled "Dear Uncle Abdul", in which Klinger writes to his Uncle Abdul to tell him all about the goings-on at the 4077th.
Peggy
trapper
The motorcycle that BJ rides in the last episode is most likely an NSU 501 Indian Scout V twin engine with a single cylinder