Sp_BlitzWho can get blocked...?
You have a couple of different questions in here.
Can sp_BlitzWho get blocked?
Yes, any query can. There are DMVs that are known to ignore isolation level requests and incur blocking.
Should I use sp_BlitzWho to log wait stats by session?
I wouldn't recommend doing that on a scheduled basis, no. If you need wait stats by session, you're better off with a traditional monitoring tool with a higher sampling rate. You wouldn't want sp_BlitzWho running, say, every 5 seconds, but you really need data at that level of granularity if you want to analyze wait stats by session.
Why shouldn't I log wait stats by session?
Because your server can be a victim of the death-by-a-thousand-cuts scenario: a query that runs thousands of times per second, each time darting in and out, and never accumulating that much wait time each time it runs. However, in total, it can add up to a big deal.