Well, i personally have completed the game a few times, and i have nearly always found that levels do help with drawing magic and especially rounding your characters off and keeping them near enough even is a high priority. At the beginning, i personally think it's crucial to have good levels, enemies such as Ifrit will nearly always have the same HP, it will only differ by about 100~200 max if you level up one level or ten.

However, the Ultimecia battle will be really easy if you keep one character at a low level (as i found on three of my games) and she only has approximately 600,000 hp at the last stage, which is really nothing to worry about. Junctioning and Levels go hand in hand in this game: junctioning gets you levels and levels get you better junctioning - its just a repeating circle. I personally relied mainly on my levels and sats all the time to get me my magic, I hate refining.
And Ultimecia really shouldn't cause too many problems!