No, hops should not be grown inside. Their roots need too much room to spread out, and a container is just not large enough to support the growth. These are not small plants when they grow. A lot of people are not familiar with what hops look like in a field, but most people know what grape vines look like. Hops grow the same way that grape vines grow. They get big, they take up space, and they need a lot of height.
A few years back we tried to grow some hops indoors as an experiment. For those that aren't aware, Midwest Supplies is also an organic and hydroponic gardening retailer. We have many (people on) staff here very good at growing herbs, tomatoes, peppers, etc. indoors. We set everything up and gave it a try. Let's just say that we ended up with a rotted-out stick by the time we were done.
Unfortunately, our customers have had the same luck. We've had several brewers try it over the years with the same luck. Hop plants are just not meant to be grown indoors. It is also not a good idea to try and "start" your hops indoors as well. Due to the timing of when we receive our hops there are several states still dealing with winter at the time. You do not want to plant hops in frozen ground. So, a lot of people ask if they should just get them started inside until the ground is warm enough to plant. Again, no, it doesn't work. Just leave the rhizome in the fridge until you can plant it outdoors. Spray the rhizome with some water every couple days and that will keep it alive. Remember that rhizomes do not need much water, so just spray enough to get it wet.
Hop rhizomes will store in the refrigerator for several months without issues. We've taken the oldest, smallest, nastiest looking rhizomes you can imagine and planted them. To our surprise, and our employees' excitement, they've grown.
Read ourCan I grow rhizomes indoors? PDF