This is actually a good technical question... because none of us really know the answer without knowing the details of the motherboard and speaker, which can only be obtained by proper testing or teardown.
in-ear headphones, especially BA drivers, generally perform poor with onboard sound because 1) High noise levels 2) BA drivers have high impedance variation with frequency, and onboard sound / sound cards have high output impedance if it is labelled "line out" and not "headphone out". That being said, some motherboards / laptops do have headphone out / line out combo jacks, but even then the output impedance is a mess, so as said in paragraph #1, none of us really know without testing.
As for the headphone jack on speakers, often (I HOPE) it is positioned behind a buffer behind the volume control so you can adjust the headphone's volume, but I'm pretty sure there are oddball products which connects the headphone out directly to line-in. In any case, the output impedance of the headphone out is often again unspecified.
Ultimately, if you can't hear a difference, it's good enough. Even in some cases where you can hear a difference, like using my old PSP's headphone out with BA IEMs, I can live with it. Especially considering any "proper" solution to fix tiny problem will cost more than your M1250.