In go, is it possible to guess the opponent's strength from their play?
Probably the best way to gauge a player's strength (aside from playing against them of course) is to present them with Tsumego of varying difficulties. From Sensei's Library:

Tsumego, a Japanese go term adopted into English, are problems mainly about life and death, but also about ko, capturing races, cutting, connecting, etc. As a rule they are local problems, but a few involve the whole board.
There are many published collections of tsumego, or life-and-death problems, many in Asian languages but increasingly many in Western languages. Many collections are available on the internet. SL also has a growing collection of go problems.
Most professional players and top amateur players agree that solving tsumego is the best way to improve.

Sensei's Library has a plethora of tsumego from a variety of sources.
Personally, I've also used GoProblems.com a lot to improve my own skills. I like that they try to associate individual tsumego with what rank should be able to solve them. They also have an incredible number to choose from. As of this posting they claim to have 11,196 problems.