Yes, the PS3 is fully compatible with SSDs, though not necessarily optimized for it. There are many benchmarks that compare the difference in performance of a PS3 using an HDD or an SSD. Also keep in mind that people have been running Windows XP (released in 2001) on SSDs without much problems either.
Most of an SSDs internal workings aren't handled by drivers in the first place, and instead are the responsibility of controller chips built directly into the SSD. Those chips not only handle file seeking, reading, and writing (and deleting), but also wear-levelling — a feature which does not exist for HDDs, as it would be useless there.
Windows 7 was the first Windows OS to feature optimizations for SSDs. These optimizations were mostly deactivating HDD optimizations that made no sense for SSDs, such as defragmentation. It also introduced TRIM support, which helped with file deletion — yet another feature that made no sense on HDDs.
If anything, it is possible that the PS3 would suffer from performance issues when deleting or writing after deletion of large files, which is what TRIM support is meant to suppress.