If you can learn to sound good on a poor instrument, you might sound great on a nice instrument. But if you sound great on a nice instrument, you will still carry those skills to the poor instrument and sound good on it. The advantage to sticking with the cheap instrument is that it saves you money, and until you are very good, it is unlikely to severely hold back your skill. If you aren't playing professionally or auditioning for high quality orchestras, an upgrade probably isn't necesary to progress.
Money alone won't guarantee a good instrument. With good luck, you can find an inexpensive instrument whose sound is much, much better than you'd expect from the price tag. On the other hand, I once tried a $3000 violin that sounded worse than my $500 violin. If you are considering upgrading, take your time. You know your current instrument. Try enough violins that you know the kind of sound you can expect at different prices.
Try violins in person yourself, and have a second person play them for you because they sound different under your ear and across the room. Have a musician who is a better violinist than you come with you when you test the violins. Shopping in person is much better than ordering through the mail. If you have to mail order, have the shop play the violins over Skype or a phone, and use that to judge the sound. Pick a shop that lets you order a few instruments and test them in person and return the ones you don't want, even if that's all of them. If you can't afford that now, then stick with your current violin and keep saving money until you can.