Hi
Is it possible to drive the LED directly over the Arduino PWM pins (4x RGB stripes)?
There is currently no pwm support in the library. You can use the math and color functions to get your rgb values however and set the pwm directly.
And I have done this successfully, as well as using the PWM outputs to drive three MOSFETs and then a strip of 12V “analog” LEDs (ie the nonaddressable kind).
Old school 
Yes, but like Mark said you will need a MOSFET or Transistors to allow you to tie into the power rail and draw enough current (if you try and draw through the GPIO’s directly it could damage the pin, burn it out or trip the resettable fuse.
You may be able to use a ULN2003 transistor array to reduce component count