My startup took a severe hit when I started a new relationship. After I married and got refocused on the business, the relationship took a hit. It has been a dangerous balancing act. My advice would be pick one, get it stable, then move on to the next one. I love my wife and I love my business and they both suffered because I got greedy and wanted both, right now.
I think having a startup and being in a relationship is the same thing as working and being in a relationship. It takes commitment and sacrifice by both people. Classic work-life balance
Yes, it is possible. Your success in anything depends on your commitment. If you are committed to your relationship and committed to your startup, you can do both. If your commitment to one or the other wanes, that will be the thing that goes when times get tough
Have a search on the forum on work/life balance and 'partners.' There are some excellent posts with great tips. Here is one I found helpful: How to start a business and not destroy your marriage? Also Steve Blank's article Launching a startup and having a family life – it’s possible! is a fantastic post from someone who's been there.
It really depends in you and your significant other. A startup is very demanding and it usually requires more time and dedication than a regular job.
You need your significant other to understand this and be willing to give you time and support for your startup. If what you have is a very demanding significant other then it is practically impossible to have a relationship and start a business.