The short answer is yes, but the slightly longer answer is: it depends on the film, and on the quality of the digital copy.
If the disc you're playing isn't 4K, your blu-ray player will upscale it. That uses an algorithm to fill in the gaps between the quality of the source material and what a 4K version would be, and the best 4K players do a superb job of this. They can't work miracles but we think you'll be pleasantly surprised by how much better your older discs can look when they've been upscaled.
The holy grail for fans of older movies is the digital restoration. That's when a classic or cult movie is digitised with plenty of care and consideration, with the goal of delivering it as the filmmakers intended. With films shot on 35, 65 or 70mm film stock, which most big-budget productions were, that film stock was equivalent to a much higher resolution than Blu-Ray (even 4K) – so scanning each frame with modern tech for a 4K Blu-Ray release can deliver absolutely spectacular results.
We say "can deliver" rather than "does deliver" because there are lots of variables in play here, ranging from how carefully the original film stock has been stored to the skills of the restorers and the resources they've been given. That's particularly apparent with remastered films released in the early days of Blu-Ray, not all of which were as good as they could have been. However, more careful restorations, such as the 11-month, 2,700-hour restoration of Apocalypse Now for its 40th anniversary edition, or the 4K Blu-ray of Casino, are absolutely stunning and make you feel like you're watching the film for the very first time.