yes it does stake on MOBILE wallet !! to add here, it downloads the blockchain so yes in that respect you need to have some space , but these days most of the phones are coming with large amount of Disk Space , Overall i would say why should one pay for VPS etc or have a CPU online 24/7 just to stake, when you have your MOBILE on 24/7 and you can stake,without using much of the Phones resources too