Essentially, yes. But this is most appropriate with sole proprietorships and general partnerships. With a corporation, generally the owner is reimbursed the out of pocket expenses either with a petty cash disbursement or on their paycheque. The personal purchases on a company charge card can either be applied against an Owner's Equity or Drawing account or a Shareholder Loans account, or the amount may be deducted FROM their paycheque.
When I put through purchases made with personal funds or on a personal credit card where the balance is NOT paid by the company, I make an expense report, breaking down taxes and net amounts, and categorizing each purchase.
I then set up the owner as a vendor, and submit the expense report like a bill from the owner. Once per quarter or year, I make a G/J adjusting entry clearing the bills and offsetting the A/P amount to Owner's Equity. This way the owner is showing the amount of cash he/she has spent/input into the company for either expenses or cost of goods, and their Equity in the enterprise is increased.
When I am entering personal purchases made on a company credit card where the balance is paid by the COMPANY, I enter the business expenses according to their expense categories and the personal purchases go against Owner's Draw. In this way, the personal purchases become a deduction from the Equity. If the draws exceed the funds injected by the owner, then the overages become taxable by the owner.
I must, however, restate as I have in the past: PLEASE CONSULT YOUR ACCOUNTANT.