How much of an advantage would it be if one side had a means of acquiring information in real time while the other side had to make do with conventional means of detection? Could the disadvantaged side overcome that disadvantage with enough skill, or would they be screwed?
Not enough information to give an answer. Basically what other technology is in the picture?
One of the difficulties of space combat is information, or rather the delay in getting it. At the distances involved, with conventional detection methods like radar, what you are "seeing" can be minutes, hours, even days old. Tactics and ship movements would have to take that into account.
Well one reason you need to know what kind of technology you are talking about is effective weapons range versus sensor range.
Right now what we could be using in the next 50 years versus how far we can detect and track things is a pretty large range. Despite light speed delay we are capable of tracking and sensing things way outside of weapons range. Each spaceship is basically a huge radiation source (primarily heat).
Anyway the go-to site on all aspect of space combat is the Atomic Rockets site at
http://www.projectrho.com/public_html/rocket/The section on detection is here and includes a section on stealth
http://www.projectrho.com/public_html/rocket/spacewardetect.phpIn general hitting a target requires developing an understanding of the target's trajectory versus the amount of delta-vee the target has versus the amount of delta-vee the attacker has. Or if you are using continuous thrust drives (real or unobtainium) the amount of time it takes to change a trajectory.
Factor in orbital mechanics the result is a series of envelopes and time windows. If the attacker makes theirs then the defender will be attacked. If the defender makes their an attack is all but impossible.
Normally it is expressed as a probability cone based on last known position and drive capabilities. With the type of sensor you are talking about then targeting solution becomes far easier as you can adjust your trajectory far sooner than the attacker. But it not a certain thing as a lot depends on the relative capabilities of the ships. Also depend on whether the defender know that the attacker has the technology.
In general it will extremely useful but not quite winner you think it would be. This is because near future technologies are used at light minutes or light seconds range. So the time lag isn't as big of a factor.
At a strategic level orbital mechanics are a factor even with continuous thrust drives