Not if the mob dies in under 11 seconds of combat, as you'd lose at least 1 tick of Rake. Once you drop a tick, Mangle scales better with AP than Rake (not to mention that you may get an extra tick applying Rake earlier).
Also, not after factoring in crits. With all 3 ticks, Rake scales by 0.19 AP, but only by 0.01 AP for crit damage. Mangle scales by 1/7 AP (a little under 0.143), all of which is in play for a crit. Assuming PI but no meta gem, buffing Mangle with SR is better than buffing Rake at a little under a 32.3% crit rate.