Speaking as a long-term Mongol Conquest army fielder.
Definitely take the artillery if you have that option.
It will prove vital against WWG and El for example. One of my favourite victories was against a Hussite army, in which my artillery element was crucial, not just in picking off WWG from out of their range, but also in luring out their Kn General to destruction.
Bw can decimate LH elements in short order and the artillery can, at the very least, knock their formation around.
Hi Snowcat, Paddy and I came up with an army which is not strictly all Mounted(but can be) and can have 2 Artillery... and is a Historical opponent of your Avars! III Maurikian Byzantines can take Khazar Allies that can also bring along an artillery piece.It's a bit pip heavy, but certainly potent.
Paddy was going to field it in a Tournement but couldn't make it and it would have been interesting to see how it would have performed.