Aloha - Amanda here. I'm a financial and tax expert, with an EA distinction (IRS Enrolled Agent). I have a master's in accounting, MBA and big four public accounting background in taxation. I've also been a tax expert for Intuit for many years. I specialize in making the complex simple, so that you can focus on what you do!
It seems your question was left unanswered and I think I can clear this up for you.
In short - I don't think you have anything to worry about because you're trying to report everything accurately. Every penny you earn is supposed to be included in your income. So being extra careful about that and recording every business deposit, as such, would actually be the accurate thing to do (albeit many don't do it).
Additionally, be sure to keep documentation for all of the amounts you report for income (this can be as simple as hand written receipts, but be sure to include dates, customer name, work provided). Of course, additional documents such as invoices, contracts and deposit slips, is even better.
To answer your question directly, YES, it is possible for the IRS, during a full blown audit, to reduce your income (if it was inaccurately overstated) and for that to be updated for SS income. That being said, it would be extremely uncommon for that to be the trigger because they are far more focused on the underpayment of tax. The social security administration is not part of the IRS. Additionally, it is far less common for there to be full blown audits these days. Instead, it's more common for the IRS to audit individual expense items on your return.
Let me know if this clears up your concern or if you have follow up questions.