Yes it will work to put a headphones output 3.5mm stereo type connection from your phones headphone output to the mic input on your computer. The output level out of the device would need to be turned down, because a mic input is not designed for that input level. I have done this before, it is just a matter of adjusting everything to the correct levels (which takes more time than connecting it).
It is "better" though to input these kind of levels of a line level or headphones output into the "line input" on the computer , if you have one of those. Line inputs are color coded blue usually. intended input levels for line inputs are +1to-1V P-P. Although computers do not always follow all the same balances and rules of normal audio. You could test both inputs if you had them. to see which one matches best.
Using the line-in for the phone and the mic-in for the mic , you could then possibly do the mixing in the computer, instead of trying to crash them together.
They do make "padding" adapters where there is small added resistance to reduce the total levels, to make a headphones/speaker type output lower in level for a mic input, that could be applied if the level is too high and turning down volume is not enough, or has more noise than level at that volume setting.
Plus there is also isolation transformers that could be used, to electrically seperate the 2 if there was that kind of noise.
Next , to add in a microphone Y-adapted to the same input at the same time. That would get more messy and more complicated, you would end up with double termination, where each one (now tied together) would effect the other. The microphone output level would be very low compared to what you would get out of a headphones output. Padding (see above) might become a desired component , to reduce the levels of the headphone output.
The style of mic , dynamic, electret, cardoid, if it is a powered mic and all will make huge differences in how the levels will match and how each input will effect the other. Usually this does not go well. It is possible that an isolation transformer (above) would help isolate that headphones output first, to better allow the mic to co-exist.
A simple mixer like a cheap analog 4 channel stereo mic-line mixer could easily be applied here, solve most of the issues, and give you full control.
Can you mess anything up, it is possible if you turned the volume level of the device up, and the device Has some pretty good output that you could damage the input, or parts of the mic, not likely but possible. Again a Mic input is not designed for the levels that are output from a headphones output, it did work better than expected when I did that here. Just reduce the volume prior to getting an ear on it, and be aware of "distortion" that is caused by to much level.
Other stuff: Most mics are mono, even if they use 3 connection points and feed to both sides, some mics only have the 2 connections, either way without isolation or a mixer, your combining will make everything mono. The mono mic will also make crash mixing of the 2 even more problematic.
