Person A seems either to be confused or to be using poetic language, as the meaning is not clear in itself but seems to reference a number of meanings and idioms:
Merriam Webster gives the following definition of "pool":
3*pool* noun:
4 a readily available supply: as
[...]
c : a group of people available for some purpose
The meaning of "pooled resources" in definition 6 is related:
6 a group of journalists from usually several news organizations using
pooled resources (as television equipment) to produce shared coverage especially of events to which access is restricted
In 4, "pool" is used to describe the group, rather than the individuals (like water in a swimming pool). The idea of "pooled" in 6 is similar: resources have been collected together (again, think of water in a pool).
So it seems that Person A is wanting to refer to a collective group of people committing false marriage, but they may have mixed this up with the ideas of
A
opening (oneself) up to (something), meaning that you are making
yourself available for something to happen to you
and
B a blowing something (wide) open (or blowing the lid off
something), meaning to expose the truth of something (usually in
reference to something scandalous): "I want to blow the lid open on
false marriages" would mean they want to expose the people (or "pool"
of people) who are having false marriages.
and/or b opening a can of worms, meaning to create a situation
that will cause trouble or be unpleasant
I think ultimately they used "pool" to give a sense that the group of people doing this (or who would do this) is quite large, and/or that they are a collective - a group with the same ideas and principles rather than individuals, AND that marriages would be "opened up to" a situation in which they happen falsely (for financial gain, etc) and/or that gay marriage equality would be like "opening a can of worms", which would cause problems.
I think that I understand the humor perfectly and I guess it's kind of funny. Your translation is totally comprehensible, but it does contain one very serious grammatical mistake. You forgot to add an ed on the end of completed. Since the verb complete is supposed to be used as part of a present perfect tense form, it's absolutely got to have it. Also, what's the point of writing some of the words in there in all caps? Please, don't do that. Having said that, here's my take on your joke:
— What are you gonna do today?
— Nothing.
— But isn't that what you were doing yesterday?
— Yep, but I haven't finished it yet.
Best Answer
"Dog" or "dawg" is a slang way to talk to a close friend (especially in some American cultural dialects)
So "What's up dawg?" means "How are you, mate?"
The joke is, Person A says "It smells like updog." (updog is a made up word). Person be doesn't know the meaning of "updog", so he asks "What's updog?" Person A has tricked person B into saying "What's up dawg?" in a casual slangy way. It is the trick that is the joke.
Don't try to emulate, and start calling your friends "dawg" it won't come across as natural.