With some rough math, we can estimate how much more efficient those cheek pouches make the chipmunk. Lets say we have two chipmunks, one with cheek pouches and one without. We can compare roughly how much time they spend in danger while out foraging.
Without cheek pouches
Our chipmunk finds a red oak tree exactly 100′ away from her tunnel. She’s quick, and can average a pace of 10 feet per second when foraging (a chipmunk’s top speed is supposedly a blistering 21mph, or 30′ per second). At her foraging pace it takes her precisely 10 seconds to get from her tunnel to the acorns. It’ll take another 5 seconds or so of handling time to find and pick up an acorn, and then another 12 seconds to get back to the entrance of her burrow (it’s harder to run with an acorn in your mouth). That’s 27 seconds of time per acorn that she’s outside her burrow, exposed to potential predators. Chipmunks store about 8 pounds (~3600g) of food for winter. A red oak acorn weighs about 5g (source), so she’ll need to cache about 720 acorns to get her through the winter. Without cheek pouches she’ll spend a total of 5.4 hours out of her tunnel collecting acorns [=27 seconds/trip * 720 trips].
With cheek pouches
Having internal cheek pouches means that the chipmunk can store a significantly larger volume of food on each foraging trip. It only takes about 5 seconds to pick up an acorn, but it takes 22 seconds to go to and from the tunnel. That same chipmunk, with the advantage of storing 4 acorns in her cheek pouches only has to make 180 trips. It might take her roughly the same amount of time to get to and from her tunnel, but she’ll spend longer outside of tunnel on each trip. If she gathers 4 acorns per trip, she’ll spend about 20 seconds collecting the four acorns and stuffing them into her cheek pouches. While each trip is more dangerous, a chipmunk with cheek pouches will have cut her total foraging time down to just 2.1 hours [= 42 seconds/trip * 180 trips].
This is a gross oversimplification of the time estimate, but the math gives a pretty clear sense of just how much time having those internal cheek pouches can save. My estimate will be on the low side as chipmunks never run in a straight line and it takes them much longer per trip to find food. One author watched a chipmunk gathering food and found it averaged about 2 minutes for a foraging trip of about 180 feet, or roughly 1.5 feet per second (Wishner). Additionally acorns are about the largest food item that they’ll store, so in all likelihood they’re making far more than 720 (or 180) trips to collect enough food to get them through the winter.