Unlike an RF splitter (which provides an impedance match to each destination at the expense of signal strength), a "splitter" when it comes to line level audio is nothing more than means of physically connecting multiple things to a single output. In other words, a "Y" cord. Each destination is connected to the output..and connected to the other destination(s). So there is no quality performance issue, other than good physical construction.
However, every audio output has several critical characteristics to keep in mind. They have a source impedance, and a maximum load they are capable of driving. Think of a source impedance as a resistor in series with an output of zero impedance. That's not exactly what it is, but it works for a basic model. So when you hang a cable on that model, you've added a capacitor (cable capacitance) a resistor and an inductor, which creates a network with a non-flat frequency response. Now before anyone freaks out, the frequency at which the response changes from flat is a function of the specifics. If an audio device has a very low source impedance, and it's driving a cable with low capacitance and low inductance, into a high impedance device (load), the break point is far, far above the audible range. This happens when we plug in a relatively short cable between two normal audio devices.
When you try to split an output to feed several devices, all cable capacitances, inductances, and receiving devices loads add. If the output has a typical line-level source impedance of 1K - 2K, cables are short, and the receiving devices input impedances are high, this might not be a problem at all. But if several devices are all driven through long cables, the high frequency roll-off point drops lower. And, if all devices input impedances added together exceed the outputs maximum capability, other things can happen, like lower level or distortion.
In professional installations single audio outputs rarely drive more than two devices, typically just one. If there are multiple destinations, some form of active distribution device is used providing each destination with it's own low-impedance source.
Back to the original question, the answer depends on how many devices, how long the cables and of what type, and the output impedance of the driving device as well as the intended use. Background music is not critical, and can suffer a bit of high end loss without notice. So likely there will be no perceived issue.
But the other problem more likely to run into is the potential to create ground loops. The chassis of different devices at some distance away and powered from different electrical outlets may be at different ground potentials. The result could be hum. There's a cure for that as well, though, and it's not expensive or difficult.
Go ahead and wire it all up, see what you get. If you have problems, stop back here and we'll take care of them. My bet its, it'll be just fine if you don't go too crazy.
Here's a cheap distribution amp
(you don't have to use the video portion).
If you get hum, here's a cheap ground loop isolator.
Note that the two devices above do not do the same thing, and are not interchangeable, but can work together.