A:
Some thing has to feed your Roku stick internet. So no, I'm sorry. A router just accepts and distributes an internet connection. It does not supply it.
"The Roku Streaming Stick takes all the capabilities of the current Roku box, the smallest of which is 3.5 by 3.5 by 1 inches (8.9 by 8.9 by 2.5 centimeters), and crams them into a tiny thumb drive-sized form. There are two versions: the original MHL version (now called the Roku Ready version) measuring 2.7 by 1 by 0.4 inches (6.9 by 2.5 by 1 centimers), and the new HDMI version measuring 3.1 by 1.1 by 0.5 inches (7.9 by 2.8 by 1.3 centimeters). Both plug directly into a television port and allow you to stream shows, movies, music and more, all via your home WiFi network, without taking up the living room real estate required by current set-top boxes."
https://electronics.howstuffworks.com/gadgets/other-gadgets/roku-streaming-stick2.htm
You could possibly use a cell phone hotspot. But not a great alternative to an inhouse internet connection.