That solution would work until direct RF from the UHF transmitter fries the FM chip's amplifiers (which is also your Bluetooth and WiFi chip). Even at only a few watts and even at four to five times the frequency, directly fed to the chip might be more than it can handle.
But then it might not. >shrugs< I wouldn't know.
Same time though, if you do go this route, you'll need to engineer a way to trigger the "headphones are plugged in" switch. I think this is a physical contact-break in the jack, but at the same time I've seen that some designs use an electronic signal to detect the impedance of the headphone speakers, microphone, etc. (especially on TRRS jacks such as are used in phones) to detect the difference between headphones, mic+headphones, or a selfie stick/camera remote shutter button.
It's possibly a bigger job than it would seem on the surface.
That Baofeng turns off the FM receiver when you hit the transmit button while listening, and there's an almost palpable delay between the receiver turning off and the transceiver keying up, then again when it switches back to FM receive. There's certainly a chip/relay that disconnects the FM receiver from the antenna during transmission.
I live in an area where radio signals are strong enough that just a short adapter (e.g. TRRS-to-TRS-headphone+TRS-mic splitter adapter) is enough antenna, and I carry one of those in my laptop bag for work. Small enough, light enough, etc. that if I listened to radio often enough I'd have no problem adding it to the numerous items I already carry in my pockets everywhere I go. Might work for you.
But I agree, the headphones-plugged-in requirement for an antenna is stupid.
(Edited for readability after editing to include a forgotten item)