Does Ubuntu 20.04 installer skip creating a swap partition?

Swap is now a file

Ubuntu 20.04 creates a swap file during installation. Swap partitions are not required anymore. This is irrespective of SSD or HDD.

Ubuntu started using a swap file instead of a partition from the version 17.04. See Default 17.04 swap file location for more.

Swap is still needed

The suggestion that you should disable or remove swap from SSD is rather old. it comes from the old time when SSDs would get corrupt with too many writes. Modern SSDs are more robust. So, it is okay to keep a swap file (or a swap partition, if you really need it) in the SSD.

I would keep the default swap file as is in the SSD unless you have some special needs and requirements. If you have enough RAM the swap file may not be used much and won't "speedup" the death of the SSD by any significant time. On the other hand, if you edit videos or work with lots of open tabs in Firefox the swap file will prevent your computer from crashing if it runs out of RAM.

Hope this helps