The main thing you have to be careful for is the speaker. The speaker in a guitar amp is designed for the Highs and mids, and too much of the low can blow the speaker. But since you'll be using headphones the speaker will be spared haha
As far as tone that you'll get from it, it won't be the best because the amp it self is also designed for delivering the high and mid range sound, even with adjusting the High Mid and Low settings that are on the amp you might not find the "right" tone.
And when you're looking for a pedal, be sure to check to see it works with bass guitars as some do not. My pedal only works with guitars, and I thought that at least the tuner would work for a bass but I was wrong.
Hope I am able to help. If you ever need advice in this area, feel free to ask. I have 15 years experience playing guitar and lugging around the equipment haha