I did this a very long time ago, but a bit differently. I lived in an upper story flat in San Francisco. The ceilings were 10' high, so the windows were quite tall. They were broad, too. I placed tacks under the bottom of the sill & on top of the frame, then strung fishing line from the bottom to the top, intending to give the vines something to climb up that wasn't really noticeable. (My bed was positioned next to the window.) This room had a southern exposure, and SF weather is temperate - so no problems with growing indoors. I grew several varieties of morning glories & a couple sweet peas. They performed well. The other vining plants (tropicals) needed heavier line, so that was a mistake easily remedied. It took a while for the vines to climb up/over to the bedpost/headboard. What I forgot to anticipate was white fly & aphids. I had thought the window screen would keep them out, but I was wrong. So, while it looked fabulous, it was an ordeal to get rid of the bugs. If your support can take the weight & the plant is not a bug-magnet, it will be worth the effort!