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I'll now hand over to our super knowledgeable members who I'm sure will be happy to chime in on this topic.
It's possible @Nanawren
Not the best idea though! Tomatoes need space to grow. Invest in a big pot or better still, a raised garden bed of some sort. Tips here - https://www.bunnings.com.au/diy-advice/garden/planting-and-growing/how-to-grow-tomatoes
I like this idea, but as you advised tomatoes do love their space and can grow big if you use a cage or trellis:)
I recommend planting in pots or a small garden bed, way better off.