Yes. Credit scoring algorithms like FICO or VantageScore rate your ability to manage different types of credit, but not necessarily where you get your credit cards from. Therefore, on a typical personal credit report, a secured credit card from a credit union looks just like an unsecured credit card from a major national lender.
Credit scores really only measure whether you're good at managing your existing credit, so it's almost impossible to qualify for an instant approval credit card offer when you're not already carrying one of the big four brands in your wallet. Retail and gas cards can help, but credit scoring algorithms often treat those as "training wheels" accounts.
When you're building a credit history, secured credit cards let you game the system. Just leave a few hundred dollars as your security deposit, then make the absolute minimum purchase necessary each month to register activity on your credit report. That usually means buying a pack of gum or an item from your favorite fast-food chain's dollar menu, then paying your balance off so you don't rack up a finance charge. The combination of positive activity and low credit utilization can boost your credit score over time with little risk.
Although a handful of retail banks offer reasonable deals on secured cards, credit unions offer a tactical advantage for your long-range personal financial planning. Banks often reserve their very best credit card deals for brand new customers with excellent credit. If you're planning to eventually earn a premium rewards credit card with a high credit limit, building a strong track record at a credit union can make you an attractive prospect.
If you've been avoiding credit unions because you think you won't get the same scale or support as a large bank, you're missing a major trend. Pentagon Federal Credit Union has grown into one of the country's largest nonprofit financial institutions, offering online banking and global support for members. You can qualify for membership just by making a one-time donation to an affiliated charity. Your neighborhood credit union may also offer secured credit cards, usually serviced on their behalf by the operational division of a more familiar national megabuck.