Britain did not actually have a treaty with Poland until 1939. Poland did have a treaty with France, and the stated position of the Polish government was that they would fight Germany over Czechoslovakia if and only if France did (they did not even consider, until September 30, the possibility that Czechoslovakia might fight alone). If Atlee extends a treaty to Poland equivalent to the treaty with France...maybe they'd fight without France, but given the small size of the British army and the fact that Poland's problems are continental, France would have been considered the more important ally.
To my understanding, Daladier personally favored fighting for Czechoslovakia, but only with Britain's backing, and much of his cabinet (especially Georges Bonnet, foreign minister) was opposed totally.
If Atlee commits to war, I think France would follow him in and Munich would end in an ultimatum demanding Germany back off, which may or may not lead to Hitler suffering a 9mm stroke and a military government.