Can I use a USB flash drive as my main OS on the Mac?

Live

You can use a live USB as your main OS, as long as you have enough RAM (+4GB seems very usable, even 2GB should work). Some unique features are:

• All new files & changes are in RAM, but are lost with a reboot.
• New software sources/PPAs can be tried & packages installed (provided you have the RAM), but are lost with a reboot.
• Any accidental errors like this are also lost with a reboot:
  • uninstalling your desktop or libc
  • breaking packages
  • erasing / recursively [excluding changes to the USB itself - mounting it read-only helps]
  • giving root access to "some helpful pal online" who breaks everything or installs questionable programs.
  • visiting the wrong website & getting malicious tracking cookies/software or messing with your web browser

This can be great for experimenting with a new OS, it's hard to permanently "break" it. Just remember to store any files you want to keep on a real partition (like a 2nd or 3rd partition of the USB) or online.

You can even update a few packages by installing some .deb files "to ram" after booting, but creating a new live USB / ISO would make the changes permanent. (There should be some tools to create a live ISO from a running live system, other distros like MX-Linux have virtually 1-click tools included).

Upgrading to a new release means just downloading a new ISO & making a new live USB.

A big limitation might be the read speed of your USB drive. USB read speeds could be from 10MB/s to 30MB/s for relatively cheap USBs, or 50-300MB/s for USB2 or USB3 devices which may be comparable to a hard drive. (USB writing speed is generally slower than reading). However, the seek times of a USB are near 1-5ms, so it may "feel" faster sometimes compared to a spinning hard drive (seek times +70ms?).

And the toram boot option could help the speed A LOT if you can spare the 1 or 2GB of ram; then all files are read at your RAM's speed (1GB/s to 10GB/s?) much much faster than a hard drive and almost all SSD's - the whole system could feel lightning fast (you'll really notice if you have a slow internet connection then ;-)

• toram can also let you use a USB drive to boot live in ram, then install to / format / overwrite / remove that same USB drive.

Live with Persistence

If you used persistence on your live USB, it would feel & act like a regular fully installed system, with changes saved to the persistent file/partition.

Now you'll have to avoid breaking your system, but even if you did a catastrophic failure, all the changes are kept in the persistent file/partition, and you can boot without persistence & erase the persistent data to start over.

The limited write lifetime of the USB's flash memory might be a concern, using the noatime mount option should avoid some generally useless writes updating inode access times (ex. mount -o remount,noatime <usb>). In practice it could take years to wear out a USB, and they're very cheap & easy to replace; Even an old small 4GB USB is big enough for most live distros.

Full Install to USB

If you're talking about doing a full install directly to a USB drive, that may or may not work. I think it depends on the particular drive, some should work, but some won't (too slow, corrupts files, mystery problems...).

A cheap brand of orange USB's (that rhyme with "Flexar") would be 100% reliable as a live USB for months, but trying a full install would slow to a crawl then crash with permanent filesystem errors. But others report great success.

Making a good backup of your data and OS-X is a pre-requisite, or at least have an install disk & code (or whatever OS-X uses) ready for a clean re-install.

You may never be able to fully overwrite a Flash memory USB, so if you'll be storing extremely sensitive data then use encryption.

Installed system in USB drive

Yes, you can install Ubuntu and Ubuntu community flavours (Kubuntu, Lubuntu, ...Xubuntu) into a USB pendrive like it were installed into an internal drive.

Depending on the UEFI/BIOS system there may be complications to make the computer boot from USB with a MacIntosh computer compared to a standard PC.

See this link, How do I get my Mac to boot from an Ubuntu USB key?

The following link, Boot Ubuntu from external drive, and links from it describes details how to install Ubuntu into a USB drive (pendrive, SSD, HDD, memory card connected via a USB adapter).

I would recommend that you get a USB 3 to SATA box and a SATA drive (SSD or HDD) instead of a pendrive. It will be much faster and also more resistent to wear of the memory hardware. If you want to install Ubuntu to the internal drive afterwards, you can use the external box and the SATA drive for backup purposes or testing of future versions of Ubuntu.

Persistent live system in USB drive

You can also test Ubuntu with a persistent live system. It is easier for testing and more portable between computers than an installed system, but also less stable and cannot be fully updated and upgraded. For example, upgraded kernels do not work, and proprietary kernel drivers will not work.

But it can be worthwhile as a first test. See the following links,

help.ubuntu.com/community/mkusb

help.ubuntu.com/community/mkusb/persistent