It depends on how much free space you have on the SSD. But yes, especially because the swap file isn't ssd-aware, you get a high degree of write amplification which wears the disk more than necessary. That being said, newish SSDs can take a beating, even under these kinds of workloads.
I think swap files are written page-wise, so as long as the start of the page file is aligned, all the writes should be aligned. (assuming memory page size and SSD page size are the same)
Does writes being aligned on page boundaries have anything to do with them being 13 base 2 orders of magnitude smaller than flash erase blocks? An unaligned page means you erase (mostly) one or (very rarely) two flash blocks. An aligned page means you erase one flash block. The biggest amplification is the 1<<13 4k -> 32MB amplification...
