My initial thought is no, but try it and let us know!
The "Powerboost 1000" you refer to, which I'm assuming is from Adafruit (part number 2465?) is rated to supply 1 amp. Of course, they say it can supply more but this will decrease as your LiPo voltage goes down. Make sure you choose a good battery that can supply 2 amps or more.
The pi4 has a recommended supply of 3 amps of current but at idle it looks like it draws maybe 600 mA. Depending on the peak current of the board during boot or whatever you'll be using it for it may...
- Not boot at all
- You could experience board shutdown due to decreased voltage from the supply
- Risk damaging the pi4 by destroying the power supply
In addition, you didn't mention what screen you're using (7", 3.5", etc.) will draw additional current!
There are ways you could reduce the power consumption of the board but why not use a higher current supply or another board?
Of note, the older pi models use less current.