Hue uses a wireless communication protocol called ZigBee, not WiFi. The hub "translates" from ZigBee to your network.
ZigBee has some advantages over WiFi (lower power consumption, strictly 2.4GHz, more plug and play, it forms a mesh which means devices can repeat the signal, lower data throughput) which is what makes it suitable for smart home devices. 2.4GHz is also what the slower SSIDs (WiFi networks) your router advertises uses, and will reach through the walls in your average house easily (e.g. how you can see your neighbours WiFi).
The range will depend on conditions (wall construction, positioning, etc) but you'll likely be fine unless there's something very odd about your house.
Assuming you'll put the bridge next to a router that is also acting as your WiFi access point (ie using your ISP-supplied router), you can try and see if you get a WiFi signal in your garage. ZigBee will work there even if the signal your phone sees from your router is weak - the amount of data it's transferring is orders of magnitude less.
If you don't get a signal to your phone from your router in your garage, you'll possibly need to rely on the mesh - that is putting a bulb somewhere between the router and the garage. This other bulb will relay the signals from the garage bulb to the hub and vice versa. Your other option would be moving the hub somewhere closer as the hub is connected to your router via ethernet and not WiFi.
TLDR: Practically, I'd say it'll probably work - hue have a whole range of outdoor lights.
As an aside, it may be worth holding out for black Friday - Hue tends to see very good deals on the online retailers.
