For onboard audio, you've got a nice rig. I always use ASUS. I have the (outdated!) CrosshaIr V Formula-Z with the ASUS Xonar Essence STX soundcard. Yes, I would say the headphones will be fine, as your MOBO onboard audio has an impedance sensor:
ROG SupremeFX 8-Channel High Definition Audio CODEC S1220 Impedance sense for front and rear headphone outputs
Supports : Jack-detection, Multi-streaming, Front Panel Jack-retasking
High quality 120 dB SNR stereo playback output and 113 dB SNR recording input
SupremeFX Shielding Technology
Supports up to 32-Bit/192kHz playback
Audio Feature :
Optical S/PDIF out port(s) at back panel
Sonic Radar III
Sonic Studio III
Read more at https://www.legitreviews.com/asus-rog-maximus-x-hero-z370-motherboard-review_199303#AeDhTLeHX6Kc87BW.99
As said no mention of an actual amp in the specs that I see but I'd try it before you buy anything. The DT 990s are on the easier to drive side of being 250ohm and they don't really scale with better equipment.
Why not give it a try? You have a good quality setup as-is. You're not going to damage anything by connecting headphones. Unless you're going for ear-splitting decibel levels, you should be satisfied. If not, get a dedicated good quality sound card which will have it's own headphone amp.