You can encourage users to run local relays separately, but very few will do that.
That said, it should be possible to do some WASM magic and run a local relay bundled with the app, at least in theory. CC nostr:nprofile1qqszv6q4uryjzr06xfxxew34wwc5hmjfmfpqn229d72gfegsdn2q3fgpz4mhxue69uhhyetvv9ujuerpd46hxtnfduhszythwden5te0dehhxarj9emkjmn99uq35amnwvaz7tms09exzmtfvshxv6tpw34xze3wvdhk6tc4uevew nostr:nprofile1qqsprwdgjszdhucrfelp3p46nhzvd5mk7gu6zxp8r0fwc4n63zv9pnspz4mhxue69uhhyetvv9ujuerpd46hxtnfduhsz9mhwden5te0wfjkccte9ec8y6tdv9kzumn9wshszrnhwden5te0dehhxtnvdakz75qcd2e