It can make a big difference, and it is important to understand why and how it's important to you.
Here's the hard reality:
Survivor bias and wishful thinking pervades these types of stories. For every Balsamiq or 37 Signals or Smart Bear there are thousands of also-rans: smaller companies that customers felt weren't quite "professional" and "established" enough to do business with, that never achieved that quirky hook or image. The founders aren't star bloggers and don't have some quirky angle that attracts followers in droves.
The phrase - "not quite 'professional' and 'established' enough to do business with" - or the equivalent - will always be thought by a certain number of customers of smaller businesses.
The smallest players have the most difficulty with establishing credibility. This credibility extends to the willingness of prospects to buy from a smaller vendor online - the trust factor of being an unknown, less established, etc.
And especially for B2B marketing to larger entities where those businesses or government offices have de facto standards for the size and track record of vendors with whom they do business. They want to know that the application will be supported five years in the future or the SaaS will continue to be available and their data will be secure. It's always sort of assumed that the larger and older the company, the more favorable the stability and safety factors are for the customer.
Consumers will not be quite that particular, but some may only trust large, recognizable names.
So this is the actual reality, and not wishful thinking of the situation.
That does not mean you crawl under a rock.
Matt said in his answer:
Present yourself well, and you will do well. And I think you'll be happier not pretending to be something you aren't.
This is one philosophy, and that has worked for many names in the startup field such as the one mentioned, or 37 Signals. It's the "boutique" model - you substitute an image of a strong unique business personality, quality, and exclusivity which cannot be gotten from a large corporate vendor.
But the other operating philosophy - is to bluntly acknowledge the inherent value and difficulty of establishing trust, and "fake it til you make it."
This can work when you have a marketing presence that looks just like a larger company's. Most companies of any size will have case studies and other in-depth collateral on their web sites if they are B2B. A really small player will lack those things and their attempts will tend to look more amateurish.
If you do your homework and work hard to build up the image of your business, your size may make no difference and you can indeed fake it until you make it. There are norms for corporate business communications that are fairly easy to emulate.
I personally think the boutique model is extremely elusive and unlike the buzz about such successes indicates, making it work is not a model wired for default success. I consider the successful implementation of a small company specific marketing image to be a highly creative outcome that simply can't be engineered deliberately.
I personally believe that a more distanced corporate presentation (which does not imply deception - you just don't call attention to being small!) is more straightforward for most people to achieve competently.
And unlike perceptions that are rampant on boards like HN, you're not stupid and you don't deserve to just fail if you can't make a boutique image work. Sometimes the right formula to come off well in this style just can't be found.
Understand these issues, and then figure out which marketing style fits the personality of the founders and company.
Finally, you may have some iterations to get this right.