Yes, it could, but the 'a' before 'see' should be omitted. I wrote: Let's go see your house, and it was accepted by Duo (Let's as the short form for Let us).
It should be remembered that the verb (be it infinitive or gerund) after 'Let's go' never takes 'to'; like: Let's go see a movie, or Le's go swimming. But 'to' will be necessary after 'Let's go' when referring to a place, like: Let's go to the zoo or Let's go upstairs.
It is up to the speaker's choice as to what verb to use and what is most comfortable for he/she. Unfortunately Duo has chosen the verb 'ver-to see as an exercise in vocabulary to learn. Your choice would have been a different verb 'mirar-to look at'.
It is best to use the correct verb meaning when translating, in order to learn all the vocabulary presented.
Thx. I've gone through the DL tree several times and now only use the refresh/practice feature which somewhat randomly selects lessons so I have no idea what the focus (and DL's bias) may be for that lesson.
I found this link comparing "ver" and "mirar" to be helpful: http://www.alwaysspanish.com/2013/03/watch-your-spanish-ver-or-mirar.html
After going through a lot of explanation about how each verb is used, they summarize with essentially:
If the English sentence most comfortably (naturally) would use "look at", use the verb "mirar", otherwise use "ver"
I agree that "home/house/place" should be accepted, especially because "place" was one of the options while this question was presented to me in the "pick a word" format! Vamos a ver can mean "We will see..." too, but personally I put "We are going to see..."
In any case, I've reported it... March 3rd, 2016