When connecting an audio input device (be it mic, guitar or whatever) to anything else, there are basically two things to consider:
The electrical characteristics of the input device. These include, among other things, the impedance and the signal level;
The scope for intermixing the signal from the input device with other inputs.
An audio interface of the kind you are considering typically takes care of both of these, by providing a) a range of inputs to suit mic/guitar/line input levels and impedances, and b) basic mixer controls.
If you plug your electric guitar into the mic input of a computer soundcard, it will "work", but the experience will be inferior: the sound quality will not be as good as with an audio interface designed to suit an electric guitar, and you will not have the ability to mix inputs.
EDIT: Beyond these two basic points, there are additional factors depending on context and in your case, since you intend to listen to the result in real time, the performance of your audio interface (computer soundard or dedicated external interface) in conjunction with your software is critical, or there will be a noticeable lag between your playing and the time when you hear the output. This is known as latency and is obviously a no-no if you are trying to listen as you play, as it would be very distracting to your playing and out of time with anything you are playing along to. A dedicated audio interface is less likely to suffer from problems of latency.
Additionally, some units come with a built-in monitoring circuit that enables an optional mode where you can listen to a direct headphone output that is not subject to problems of latency; while this can be beneficial for monitoring the raw signal of your playing, it obviously bypasses any signal processing your software is doing, so would not help in the specific case of listening to your live playing through different DAW plugins, but you could still compare the effects when playing back recordings (or use full monitoring mode if latency was ok).