There should be no relationship between the display and the signal generator.
If you want an inbuilt AWG then you need to select a SDS1000X + (Plus) model and they have 16 ch MSO capability too. These units all come with the Decode option free ATM.
In answer to your wonderings on use of the AWG at the same time, yes of course you can but the waveform is not displayed, you have to feed it into one of the channels if you want/need to see it.
Ok, i was just guessing, still it would be handy some internal routing to a ( extra/virtual ) channel.
@ tautech : to bad the 16ch cable is not included for free.
Yes the Siglent is looking good also, only made in China makes me think twice,
what i see in the movies is the build quality of R&S is superior to others, made in EU.
The Rigol looks bad quality to me, i dont trust in the long term, i rather buy Siglent or even better, GW-instek made in Taiwan,
its about having cheap or expensive brand, i am very carefull with my stuff, if it breaks its not my fault, thats why i rather not buy cheap China brands,
it is very attractive, i have enough money for chinese brands already, one mouseclick away.
If you wanto send me a demo model for lending on your risk, maybe you can convince me as Siglent distributor.