A hard disk is just a device for storing data. The data is stored as magnetic 'bits', and either a bit is off, 0, or on, 1. Whether a bit is on or off makes no difference to the speed at which the disk spins, and no difference to how fast the platter, (like a gramophone needle), moves back and forth along the disk.
The disk spins and the platter moves back and forth so fast that it barely matters where on the disk data is stored. Fragmented files may have bits of data separated around the disk, where un-fragmented files have most of the bits close together. But we users simply cannot perceive any difference in seek and read times as they are in micro-milliseconds. For music and video files we would see no delay at all.
We might consider that the hard disk is full already, even from new. A new disk will be full of zero bits. Only as data is added are the bits changed as required to sequences of 0s and 1s. So, whether a hard disk has 'files' stored on it or not is irrelevant. The process of the Operating System, (OS), or more accurately, the 'Disk Operating System', of finding data from a disk for some specific action needed by the OS does not depend on how full the disk is.
So the way I see it, storing files on a hard disk does not slow the computer down. It matters not whether the files are personal files like music, video, photos, etc, or system files like applications, games, and so on.
However, (there is always a however), it makes common sense to 'manage' hard disk space. The OS needs free space on the hard disk for it's own use. The most common needs are Virtual Memory, (also called the Page File), and temporary folders, like Temporary Internet Files. We always recommend that the system be allowed to manage Virtual Memory disk space which will adjust itself continuously.
If a hard disk is completely full, or so close to it that very little else can be added, then your OS will start to complain and you may well see a drop in performance. But a 300 GB drive is huge, and can store thousands, if not hundreds of thousands, of single music tracks comfortably, so unless your library is massive, or you are continuously installing huge applications or large video files without 'housekeeping' you will not see any problems in the near future.
Don't forget what others have told you. With no backup copies, (more than one backup of each file), what will you do if that hard drive fails?