There are certainly corporations that think they can.
I know many of my tax and accounting brethren are shouting “NO!” In response to this question.
My answer is more on the fence.
It depends on what your corporation is up to.
If you’re a simple service provider, with money coming in from a few clients and money going out in the form of a few basic expenses, a spreadsheet to keep track of everything would probably work just fine.
Keep in mind, you should have a separate bank account for your corporation (I’ve seen corporations — especially S-corps — that don’t!), and that bank account should be reconciled.
Unlike sole proprietors, where (at least in my opinion) a balance sheet doesn’t need to be maintained, a corporation needs a balance sheet to be created at least yearly. This is possible using a spreadsheet to keep track of income and expenses, as long as there’s a reconciled bank account.
But just like with using Quicken, a business can quickly outgrow a spreadsheet, for all the same reasons a business would outgrow Quicken.
Keeping track of assets and payroll, and cost of goods sold, and actually managing accounts payable and accounts receivable is difficult if not impossible in a spreadsheet.
Just like anything else in running a business, there comes a time when you might have to invest some money in software (or — GASP — paying a professional to help!) so that things get done right.