Unfortunately the power LEDs lose efficacy, and are often limited to a ratio of 150% = Ipk/Idc_max current so that the thin wire bond does not fuse open or the current density on the chip is not excessive.
Thus operating the LEDs from 0 to 33% duty cycle at 3x the rated current will compromise the chip specs and lumen efficacy if you are expecting full performance.
Thermal design of 10 deg'C/W case temp or less is also critical for 3 Watt chips.
But operating at 0 to 33% duty cycle at 2x the rated current gives an average of 2/3 rated DC power which will work but at compromised brightness.
So it depends on your specs. Yes but sub-optimal.
A better approach is to choose a buck choke PWM regulation design for each LED and use a current shunt R to detect \$I_f\$ for each LED. A reverse clamp diode with a <50mohm RdsOn can work with a 0.5A low DCR SMD choke.
I presume that 3.7V means you intend to use a LiPo cell but that drops to 3V , so none of the linear solutions offered will work.
Let me give you another hint. This one has a range of 5000 steps on each color using PWM with inductive constant current regulation and a 50mV current sense.