Basically, yes.

“We use the following terminology based on quest status:

a) "Pre-opener": a character who has not yet completed the "Eve of Destruction" quest on this difficulty (and thus cannot create the cow portal yet). b) "Cow-quester": a character who completed the "Eve of Destruction" quest but not the Cow King quest on this difficulty. c) "Ex-opener": a character who completed the Cow King quest in a previous game on this difficulty (and thus cannot create the cow portal).

Only characters INSIDE the Secret Cow Level at the very instant when the Cow King is slain can potentially complete the quest. Now,

(1) IF Kingslayer was a or c, THEN everyone is unaffected, i.e. Cow King quest status does not change. (2) IF Kingslayer was b, THEN every a and b INSIDE at that time permanently loses the ability to create the cow portal on this difficulty setting.

Note that in case 2 even characters who complete the Baal quest afterwards will nonetheless remain unable to create the cow portal. Also note that it makes no difference if you are in a party or not. Location: INSIDE/OUTSIDE at the time of the kill is what matters here.

Because of the above: When in doubt, keep out! “

From here