However, as I've marked the work experience as "ongoing" on my resume and various forms, I'm afraid some reviewers may look negatively upon a "current job" like that, which may require constant work - perhaps they see it as a possible interruption of the internship. I've got a research lab as well on my resume, but those don't imply working over the summer. I hope they'd be reasonable about knowing that it doesn't interfere with work (it requires nearly no maintenance), but perhaps something like this is considered poorly especially for a student summer internship. They might want a majority of my time and for me to avoid distractions like managing a business. Any thoughts on the matter?
Basically most everyone does their work when studying g there's no differentiator there. Some small few take that learning and create work for themselves. Maybe it makes money, maybe not. But the learning that happens when you take a product to market is enormous.
If you were applying to be my intern, not only would we spend quite a lot of the interview talking about your project, but you'd have to be pretty terrible not to get the post.
I know we're not normal, but we'd also encourage you and see how we can support your project. Perhaps we're different though because we started the business, and grew from nothing, so we understand what it takes.
So my advice is leave it on. Some places may mark you down, but frankly, you'd get less value interning there anyway.
And assume (and tell them) you'll only be working on your SaaS after hours.
Congratulations on the effort though. Whether you get interned or not, running your own side gig makes you more employable in the long run. (and sure, you may end up closing the side-gig when you start full time work, just because you need time for a life as well :)
That's not a "might."
If you are working for a company, you are working for that company.
If you are administering your SaaS tools when you're supposed to be working on a ticket, or in a meeting, this will be a problem. If you are using company resources (computer, network) while working on the SaaS, it will be a problem.
Putting it on shouldn't hurt you if you are able to assure the company that you are able to separate the two and your SaaS will not interrupt or disturb you during working hours.
Having an issue with the SaaS interrupt or disturb you during working hours could (regardless of if you put it on the resume or not) could have anything from a "that's ok", a stern talking to, a negative reference, being let go, to a talk with legal.
Personal projects (and side companies) and the company you are interning for should never overlap unless given explicit written permission by your manager - that includes time, resources, and equipment.
Every interviewer asked me about my side projects and the tech aspect of it. The fact that it was used by 5k+ users at that time was always met with amazement and appreciation.
At my current employer, I was told that me trying things out and learning things on my own (demonstrated by me growing my SaaS) was one of the big factors in me getting hired there.
[All my interviews were at startups]
Of course once you are employed you should follow this advice
Detail out your experience as skills in your resume instead.
You have the knowledge and abilities.
Present those skills as gained from previous projects that aren't active.