Short answer: No, you do not need to buy filters.
Long answer: Unless you already have a dichroic head head with built in filters, you may want to go ahead and buy the Ilford filter pack anyway if you want to make use of the contrast control. [Multigrade paper is usable without filters. The filters just give you more control/choices from the same paper stock.]
Using colour control LEDs is a bit of an uphill battle, but it can be done if you're willing to work around some of the shortfalls of it.
First hurdle: Establishing values on the LED that map to the filters. You can sort of guestimate and ballpark these, but the results tend to be sloppy. I have yet to read anything from a photographer who has managed to get a complete 1:1 mapping for all grades of filters.
Additionally, you may run into issues due to bulb to bulb accuracy if it comes time to replace it, updates are made to the control software, or even just as the LEDs and their power controllers age.
Second hurdle: Exposure timing and rigging to your enlarger's system. You will either want a shutter controlled exposure timer, or will have to be very careful with your selection.
Some bulbs may vary in their power-on-response timing to get to the set colour temp, while others will simply turn on with a default white-light setting each time they're powered on and wait for commands to change. [For example, last I had heard, Philips Hues defaults to white when power is applied.]
This will make it rather hard to use with most power-based exposure timing systems that turn the bulb on and off for exposure.
Filters will last for years if treated carefully, and remain reliable and consistent out of the box while offering even steps of control.
In summary, if you mainly want to make prints, buy the filters. If you want to tinker and experiment while making prints, then explore and play around to see what you can do.
