G'day Glen,

You could physically do it, but all our Self Inflating mattress brands have advised warranty is void for roof top tent use.
Self inflating mats are designed to be rolled for storage, not folded. With the compression and pressure of being folded in roof top tents the bonding on the mattress and the integrity of the foam at those fold points can cause issues.
We've had a few warranty claims that have been rejected for this reason.
They're also subject to greater temperature fluctuations stored in a roof top tent - even in flat hardshell roof top tents we see alot of delamination of the glues and bonding on a mat.

Again, you can physically put a mat in your roof top tent and leave it if you want to, as long as you're aware that it won't be covered under warranty.  A good quality self inflating mat can be abit of an investment for people, so taking them out is the way to go if you want a long life from your mat.

G'day Brendan,

The Supreme Snoozer is fairly new to the market, so we don't have much feedback on these as yet.
The EXPED is known to be the "rolls royce" of sleeping mats, with the Mostamat being around for years and being one of the most popular mats we have.
The Supreme Snoozer looks to be a good quality mat, and its comfortable aswell - time will tell how it sits in the range.

G'day Romy,

We'd probably recommend the Flextail Max Pump 2 Pro 4−in−1 Portable Rechargeable Air Pump, its nice and compact, but powerful.
Fairly new to our range, but incredibly popular.
Hope that helps!

G'day Justin,

It will, but you'll need to remove the mattress for pack up - self inflating mats can't be kept inside the roof top tent between uses, as it can cause damage which won't be covered under warranty.

G'day Mollie,

Yep, it does!  Its going to be one of your better options, as most other mattresses are around 1300 wide.
This one should fit perfectly, but just make sure you flip the valves around to deflate when you want to roll the swag up - it will make it alot easier and keep the overall pack size of the swag down.