Possible, yes, advisable no, as David just commented.
You'd have to choose the resistor to suit the case when only one LED is on so that the lesser of the max currents for a Pi I/O pin and for the LED is not exceeded. Then when more LEDs turn on the available current would roughly share between them, all becoming dimmer. However the one with the lowest Vf will hog more of the current, and as Vf is temperature dependent, even if you carefully select LEDs from a larger batch for closely matched Vf, the one that's been on the most will be warmer, so will draw more current and stay warmer and brighter. TLDR: Its a mess!
However, as you can get an array of four SMD resistors in a package as small as 1.4mm x 0.6mm
(Panasonic EXB resistor array series), bite the bullet and give each LED its own series resistor.