I get Diamond Head sopranos insanely cheap, so I have several around the apartment. I have 3 restrung with different strings, and yes, it can change the sound considerably. Aquilla strings will give a Diamond Head a "bright" sound that is loud, clear and crisp. GHS strings give them a slightly different tone that I've always described as "mellow" and they are not quite as loud as Aquillas (but still a big improvement over the trash they put on them at the factory). The other is strung in D, so I can't really compare it, but the change did improve the sound quality.
On the other hand, I used to have an old Rogue uke that changing strings 3 times didn't help. To be fair, I bought it used. There may have been some unseen issue that just made it sound like crap, it could have been a bad build, or it could just be that Rogues suck. I don't have enough experience with Rogues to make that call, lol.
Economics clashes with art on this one... Every ukulele, even the cheap ones, require some minimal hand crafting. That really can make a difference in the instruments, even when they come from the same source. So, sometimes the cheap ones will surprise you and give you a better sound than their more expensive counterparts. With cheaper models, i think more often than not they are just not worth the effort to deal with for most people. Better instruments tend to command a higher price, and if the low end ukulele manufacturers had a reputation for consistently good quality their ukes would be worth more.
Whether it's factually true or not for this company or that, low end ukes have a reputation for pretty consistant bad quality. The real issue is whether or not it's worth it to experiment with yours to find out if you have a good one.