No. "Wir gehen" would mean 'We go/are going'. The verb is usually in the second place in a simple statement. When asked a question or used as a command, it is used in the first. "Gehen wir?" is the correct form. Colloquially 'wir gehen?' might be sometimes accepted but there ought to be an inflection at the end denoting that it is a question: 'Are we going?' and not a statement: "we are going"
Laufen wir? would specifically refer to your means of locomotion, i.e. "will we walk/run (as opposed to, say, taking the train)?"
Gehen wir? could either mean specifically walking, but it can also mean more generally "shall we go/leave/get going?" -- start walking out of the room even if you then intend to take a taxi, for example.
The verb is usually in the second place in a simple statement. When asked a question or used as a command, it is used in the first.
Wir gehen. : We are going. (statement)
Gehen wir. : We are going. (commanding way)
Gehen wir? : Are we going? (question)
"Gehen" may be used after the noun when there is a handler in the first place denoting that a question is being asked.
"Wollen Sie gehen?" : Do you want to go (polite form)