Nope, it's not necessary to play them in order.
Here's a quick rundown:
Circle of the Moon: GBA launch title by the team that made the N64 CV games. Non-linear game in the vein of Symphony of the Night but with far few RPG elements, more restrictive controls, simpler animations, etc. The music is mostly remixes of older tunes but the sound quality is okay and they picked nice tunes to reuse. It's not nearly as polished as the others but it's fun in its own unique ways and a lot of people really like it.
Harmony of Dissonance: the first IGA game since Symphony of the Night, and heavily reminiscent of that title. The controls are much more fluid and the visuals are a lot closer to SOTN's level of detail but the palettes were specifically chosen to look good on the OG GBA's non-backlit screen, so they look quite garish on VC or any other platform with a backlight. The quality of the music also took a hit in order to lessen the load on the CPU, so the music sounds like something from a Game Boy.This one seems to be the least popular of the GBA games but it's not bad by any means, just obviously compromised by the limitations of the hardware. (The map design isn't great, either.)
Aria of Sorrow: the second handheld game by IGA's team and widely considered the best post-SOTN Castlevania game. It looks great on any screen, the sound quality is much better than Harmony's, there's a cool new levelling system that lets you gain new abilities by collecting the souls of enemies, even Soma Cruz is kinda cool in a dorky anime sort of way. If you can only get one GBA CV game, make it this one.