No, Pi's are not a good fit to long duration battery operation.
Something like an openwrt platform that uncompresses a root ramdisk from flash might work, but the mobile network is typically missing there too. And while they may consume only a half watt they typically lack a sleep capability.
A phone is about the right combination of parts and power management, the main question is if the operating system will let you do everything you need to do this reliably. A legacy Android device, particularly something with good support for customization like a Nexus device might fit.
The other potential stumbling block is if you can get it to start up after a power loss without pushing a button; this is often dictated by an auxiliary mcu core in the SoC or by an early stage bootloader or initrd that implements a "chargingode" with no UI stack running. If you can get past that, a boot receiver on stock android might be all that is needed to get the app going again