I don't think Babcock is a coach that would purposefully lose games within the context of a game, i.e. - he won't coach his team to lose. The Leafs are losing because they are bereft of talent as their team has been systematically torn apart as part of their rebuild, but they can still win games and Babcock isn't going to tell his guys not to try that hard to score a goal for the sake of better draft position.
Especially now with them having called up a few of the young guys who are the future of their team, he'll let them go for it and I think after a close one against the best team in the league last night, they could be hungry to get a W tonight.