Yes, but I wouldn't recommend it. Bitbucket really likes fast storage and S3 is anything but fast.
S3 is not normal block type storage. It's essentially an API web service, so you need a special tool in order to mount it like block storage. Check out the s3-fuse open source project that allows you to mount S3 storage as a block device on linux. There are a few gotchas to mounting S3 as a volume on linux, so if you are really going to do this, I can give you a couple points to watch out for based on my experience.
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