Short answer, no.
We designed Quicken Simplifi to stay in sync with your bank's balance, allowing you to enter missing transactions, delete transactions, or even add transactions further back than initially downloaded. A running balance column would remove that flexibility and require users to reconcile balance discrepancies.
While we don't offer a balance column, Quicken Simplifi does have a projected balance at the top of your account registers. Click any account in the web app, and Quicken Simplifi will show you those projected balances as a graph. If you're using your phone, tap any tab and check out the row of upcoming transactions. Below each upcoming amount, you’ll see your projected balance.