Any switch that does not support multicast itself will work by instead broadcasting a multicast frame to all its ports; that's normally not a big deal, since for instance it's common to have non-multicast-aware desktop switches (at the level of an office or cubicle) at the leaves of a network served by a multicast-aware core. In that kind of situation, the ability of the core switches to restrict traffic to only the ports which have a client subscribed to the multicast group is still hugely beneficial. But then, most desktop switches degrade reasonably gracefully if they have a low-speed port attached: it's the odd piece of equipment that doesn't behave well which is the challenge!
Whether enabling multicast will or won't help in your situation or not really depends on the precise location of whatever piece of equipment is slowing things down. Machines in low-power states are just the most common nowadays; old network printers or someone hooking up a dusty old 10Mbit switch somewhere were common culprits in times of yore. To be effective in avoiding problem equipment, your network has to be arranged such that the multicast-aware equipment is able to prune the parts of the network with the problem equipment from receiving the image traffic.
So, "it depends". That said, multicast is usually best to use if you have it available: even if it doesn't solve speed problems out of the box it can be a useful tool in figuring out where problems lie (which is awfully complex in a multi-tier arrangement) because it still narrows down the scope of the high-load traffic. With multicast you can by testing often narrow down a problem area to the level of a port, whereas with directed broadcast the finest grain you can see is a subnet.
Ultimately, though, your problem could just as easily turn out to be resolvable by the old Mk.I eyeball watching the status lights on a switch rack, which could lead you to a cube or office with some piece of ancient hardware causing the trouble - looking at performance counters on the core switch is the high-tech equivalent, but sometimes it can be just a matter of spotting one small anomaly. Or not, if this is a general problem with one particular second-tier switch and low-power equipment. Unfortunately since it all tends to result in the same symptom from outside the network ("it's slow"), we can't distinguish these situations.