In short, no.
We specifically designed the Swytch kit to sit on the handlebars. This was primarily to make sure that it could be fitted and used universally on 99.9% of bikes.
Moreover, it allowed us to design and engineer the patent-pending Swytch Quick Connect Bracket. This feature is important because it means that the battery, electrics and LCD screen are all instantly removable. You need our Quick Connect Bracket to use the features of the Swytch kit effectively, which is why you cannot have it in the Brompton bag!