I'll not go into detail - but to be successful you will need to use several techniques to minimize writes to the USB flash
These include things such as (no particular order - just what comes to mind)

1) reducing the amount of logging - edit /etc/rsyslog.conf - and similar logging config options for other programs
2) creating a memory drive for the remaining logs (lost at power-down/reboot) - optional
3) if using ext filesystems - specify noatime option in /etc/fstab (not necessary for xfs)
4) don't use programs that are memory write intensive such as the squid proxy disable others eg updatedb
5) set /proc/sys/vm/swappiness to zero
6) install plenty of memory to reduce swapping to practically zero
7) use a really good quality USB flash drive - no cheapies

I'm sure there are plenty more hints on the web if you do a search

As for is it possible? - can your BIOS boot from a USB drive?
Safe/Wise? That's your risk assessment. As a minimum once you have completed the install use "dd" to make a complete copy of your USB flash drive onto another identical USB drive. Do NOT copy the drive running the current system - for instance use the install USB drive and use the option to get a command line.. This requires 3 USB drives...
1) The one you booted from
2) the one you are copying - completed installation (using dd) FROM
3) the one you are copying TO
Make sure you know which is which :-)

Should give you food for thought...