I think you shouldn't.
First the following metaphor: let's say big saas web apps are complex cars, and your small one is a bike. For sure you can't sell a car without support in case the car has a problem. For a bike, you can consider selling it without support because a lot of people can repair a bike. But a lot of people can't! All these people won't buy your bike, because they'll know in case of problem you won't be there.
Here come what is called conversion (converting people willing to buy your product to people who will actually buy it). You'll have a low conversion rate in case people know they won't have support in case of problem - and in fine you won't have a lot of sales.
At last, a very important consideration speaking about saas: be sure people WILL have problems. Too many browsers, too many OS, i'm pretty sure you didn't test every environments, just because it's a lot of work in itself.
So no you shouldn't!! As BrianAdkins stated, some great products exists on the market to help you have a descent support system. He cited zendesk, another one is UserVoice. Get an account on one of these, and spend a few hours to make a knowledge database that you will feed time to time with new users feedbacks. You'll see a huge difference in your sales.
You'll find out, I guess...
I'd at least set up a support email address to yourself and possibly an email form.
Support doesn't have to be expensive or hard...get a cheap zendesk account and use it to develop a database of answers to the questions you get. Soon people will be able to find the answers themselves and you'll get valuable feedback to help you improve your saas product.
Since you are offering a service, it makes sense to have great customer support. Having a great customer support will mean that you will maximize customer retention and get more customers because you're current users are happy where they are and tell their friends. Having your business validated by a customer means much more than self-validation or validation from your friends, loved ones, or investors.
It is okay to tell the customer before hand that you will be providing no support. I suggest however, you try to add even a least bit of support such as FAQ.
I'd say "yes" - mostly - but only if you do ALL of:
I believe if you do all of the above, you'll be just fine with near-zero support.