Would a 4G LTE sma antenna work to pickup 800mhz?
Yes it would work - but so would a paper clip.
It's the wrong wavelength.
Mobile 4G network uses several frequencies:
700 MHz (Band 28 - Telstra / Optus)
850 MHz (Band 5 - Vodafone)
900 MHz (Band 8 - Telstra)
1800 MHz (Band 3 - Telstra / Optus / Vodafone)
2100 MHz (Band 1 - [a small number of Telstra sites] / Optus [Tasmania] / Vodafone)
2300 MHz (Band 40 - Optus [Vivid Wireless spectrum])
2600 MHz (Band 7 - Telstra / Optus)
You're better off with the stock antenna or an external scanner antenna.