What is your POD? The closest Ukraine came to independence before 1917 was in 1648-59, when the Cossacks ruled half of Ukraine, but even then, southern and eastern parts of the country (where most of our coal and half of our farmland are) were controlled by the Ottomans (including their Crimean Tatar vassals) and Russians.
Even if the victorious Cossacks/some other independence movement manage to take at some point and then hold until 1913 all the land that is now known as Ukraine, and economic development proceeds as OTL, Ukraine of 1913 was a rather poor country (even if it was richer on a per capita basis than most ethnic Russian provinces), with its total GDP being somewhat larger than that of Spain, but smaller than that of Japan (and much smaller than that of Italy, famously the weakest of European great powers). Of course, Japan managed to become a great power of sorts by 1905 despite having a relatively small and backward economy. Still, to become a true great power by 1913 (and to do so in Europe, where density of great powers was the world's highest, unlike in the Far East), Ukraine would have to get a much larger economy, which probably means an earlier industrial revolution, starting at some point in the early 19th century.
So, the answer to your question is "probably, it can, but it would be a very different Ukraine."