Yes and no. If you have same source and sample it to 48kHz and 96kHz, you won't hear any difference. Your dog would, as they hear much higher, but you won't. It's physics and biology. So no need to waste resources on that if on budget.

Problem is with the source. DSP filters and distortions tend to introduce "false signal elements" called aliasing that are not supposed to be there. Good plugins oversample the signal (= raise it to 96k or 192k or higher) internally, so the DSP parts prone to aliasing will generate it way higher then is your audible range, thus you don't hear it. (...and then they downsample it back.) Theoretically if you use lot of oversampled plugins, all that resampling may actually eat more resources than just switching the daw to 96k. ...but from your description, that is not the case.

I personally switched to 96k, so I don't have to solve plugin oversampling too much. It's essentially 2x oversampling the whole DAW. But be careful if you want to do this. Suprprisingly A LOT of plugins don't like sample rate changes. They either crash, or they have badly written DSP that relies on samplerate too much and they change sound when you switch. So if you're not sure that your computer can handle it, stay at 48k. Honest advice. It will save you trouble.