Would it have been possible for the Romans to lose the Marcomannic Wars
There would be various way for Romans to loose them : are we talking a crushing defeat, or just the Roman unability to really defeat the various Barbarians? In which part of the wars : early on or in the last years?
Note that Romans, while victorious, had to withdraw after several campaigns, eventually content having made their point.
If we have an early death of the emperor on the battlefield, as propose
@GauchoBadger , then it would have decisive political consequences in a worst-case scenario (possibly entiering in a similar crisis than at the death of Commodus, with an usurper as Septimus eventually taking the purple). If we're talking of the failure of one of the later expeditions, much less so.
If so, how bad might the aftermath be for Rome? Could much earlier barbarian kingdoms have been established in the Roman Empire?
That would be extremely unlikely IMO. Barbarians chiefdoms weren't as bent on settling in Romania than raiding it
Now, the early militarisation of Barbarian peoples and coalitions wouldn't be challenged, and you might see a really important pressure on the Danubian limes that would force relocating significant forces along the region for strategical reasons, as IOTL but earlier, which would have consequences on the Parthian wars.
Furthermore, while Barbarians still at this point acknowledged the authority of the emperor in interfering with their inner matters (such as having dominance over their kings, even if it had to be stressed at sword point), the prestige and credibility of imperial authority among them would be lessened, meaning less breathing room for Rome during these raids.
Nevertheless, Rome would be too strong yet, even in crisis, to really be unable to defeat raids : it would take her more ressources and more times, but control of the territory is largely eexpectable. I said more costly because instead of taking auxiliaries among Germans as IOTL, you might have an stronger use of Barbarian mercenariate.