If I was to
chmod 777 blah.sh on server A and then move it to server B, would it retain the permissions, or would it default to some other permissions once it hit server B?
That depends entirely and completely on the method of transfer.
rsync will preserve permissions with
-p, ownership with
-o (using numeric id only if you pass
-rlopt, unless you negate it with
scp will not normally preserve permissions, but will if you pass
cp has roughly the same flags (
-p for permissions,
-a for everything and recursing).
tar has the
-p flag as well.
cpio will always preserve permissions.