can you put all the functions of an avr into a pc? no, not at all. an avr is a high power amp, dac, sound processor and analog/digital switchbox in one unit.
can you get by without an avr? sure, maybe depending on what you want to connect and what your sources are.
situations where you do not need an avr:
*pc is the only source of audio and you intend to use pc speakers
*pc or single other source are the only sources of audio and you intend to use pc speakers/similar with spdif and analog connections
*you have either a single source, multiple analog sources with switchbox, or digital sources translated to analog with adapter and as witch going to an amplifier with stereo speakers.
*you have a set of powered hifi speakers you want to use and have all analog inputs or adapters to translate to analog inputs. connectivity is easier with an avr and unpowered though.
*you want to play audio from multiple sources at the same time over a set of speakers. avr are not designed for this, and neither are pc speakers. things might get a bit ugly on the connections end if you want to do this (such as playing ps3, pc and other audio over the same speakers at the same time)
situations where you do need an avr:
*you want to use unpowered home theater speakers (which are far better than pc speakers). why avr? quite simply a five channel amplifier is expensive and for proper connectivity the adapters are also expensive if you intend to multi-source. its often cheaper and easier to use an avr.
*you want to connect multiple sources up to the same display and sound system in the simplest, cheapest and easiest way possible
*you want to utilize hdmi(arc) to get audio from a tv
a real life example...
you have a pair of speakers like the pioneer klipsch icon kb-15 and an amplifier like the dba-120 and only care about good quality stereo sound. you do not care about a subwoofer signal and stereo sound is fine. such a setup would work fine with pc and even other inputs if you had a 3.5mm or rca switchbox to route audio to the speakers depending on what source you are using. for certain devices you might need either an optical audio extractor or for hdmi(arc) a hdmi audio extractor with arc compatibility to pull analog audio from them. fairly simple setup. its possible to do similar for 5.1, but it starts getting more costly and more complex with many more cables.
you have a set of speakers like the monoprice 10565 and a cheap receiver with 5.1 support. hdmi output from pc and passthrough to the tv for video. audio from tv (if supported by hdmi(arc), optical out or analog output jacks) is also easy. other sources connect like a breeze and switching between them is also easy. simple access to upscaling 2.1 to 5.1 (pro logic) and equalizer settings as well.
i personally use an unpowered hifi system paired with a receiver for my pc, ps3 and other sources. pictures in signature link and description if you hover over my avatar for build list. while large, a receiver works great if you use one input at a time.