It is highly likely better quality components will result in a different sound experience. There will likely not be a significant change in the FR curve. Only you can decide if any difference is to your liking. Air core inductors and good poly caps will require much more space. For example, a board for woofer and a second for mid and high components.
Cyril Bateman did extensive analysis of capacitor types back in the 1970s. He showed different types of capacitors do perform differently in circuits. One clear conclusion reached was electrolytic capacitors should not be used in audio crossovers. So why do they appear in so many speakers regardless of retail price. They are cheap and compact in size. Manufacturers also know the vast majority of buyers will never disassemble and modify their speakers. If a buyer wants better sound quality, the manufacturer always offer a more expensive model claimed to be better - still with cheap parts.
A well regarded speaker designer from the 1980s-1990s, John Bau, openly discussed the price point pressures of speaker design. His designs were at the time, still are, highly sought after. In an interview, Mr. Bau suggested replacement of electrolytic caps with poly caps because of deterioration.
My experience covers upgrading three different speakers - inexpensive, mid-level, and multi-thousand dollar. All had electrolytic caps, iron core inductors and sand cast resistors. The most expensive speaker crossover was no better in quality than the inexpensive model. All three speakers had a good sound for their price point. The most expensive claimed the flattest FR curve, with an accurate sound quality. Unfortunately sterile in nature making every type of music sound lifeless.
All three were upgraded with good quality parts, not expensive or boutique. All three produced more natural sounding music with wider dynamic range. A grand piano sounded grand, not like a tinkly electric. Cymbals were crisp and clear. Bass full, no longer muddy. These were differences noted by comparing modified to un modified speakers each time.
If you want to tackle modifications, it will be a learning experience and hopefully enjoyable results.