I have a computer with 2 harddrives. The main one is an SSD, this one has premiere installed, The other one is an HDD, this one holds all of my raw video and audio. Will my video/audio coming from an HDD affect premiere's performance, or will there be no effect? (All exports will go to the HDD as well)
A system is as strong as it is the weakest link.
So yes, an old-fashioned spinning drive can hold you back.
Will it hold me back in the actual videomaking process? or just export times?
Your SSD will have a throughput of anything between 400 & 2000 MB/s. A single spinning Hard Drive will give you somewhere around about 90MB/s to 140MB/s. Effectively you are looking at at least around 4x faster throughput from an SSD.
Download the free Blackmagic Design Speed disk app if you want to see what speeds you are getting.
Can you edit from a spinning Hard Disk - yes. Will it be OK for editing - maybe. Depends on how complex your projects are. Lots of audio tracks and multiple layers of video will tax a drive more than a simple edit with few layers of audio and video etc. 4k video is going to tax an HDD more than HD footage etc.
Work with what you have and aim to get an additional SSD when you can.