That's what it means in this context. Usually "și" corresponds to the conjunction "and", and in this context it sort of carries the same meaning. For example:
They have strawberries and bananas. We also have dessert with chocolate.
Ei au căpșuni și banane. Noi avem și desert cu ciocolată.
Like "also", "și" marks that we have all the things they have plus dessert with chocolate. You can also do this by repeating the list and adding emphasis on the conjunction:
They have strawberries and bananas. We have strawberries, bananas and dessert with chocolate.
Ei au căpșuni și banane. Noi avem căpșuni, banane și desert cu ciocolată.
I hope this makes it less counter-intuitive.
That word order seems somewhat awkward in English. But I disagree with potestasity that "also" in English necessarily implies an additional dessert. It can also be understood as implying "we as well as they have a dessert with chocolate."
And I think what you are trying to do is differentiate between also applied to "we" and also applied to "dessert".
I wonder if the Romanian și in this context can be also be understood to apply either to "Noi" or to "desert"? Or would Romanian place the "și" in front of "Noi" if it was intended to refer to "we as well"?
Yes, in the original Romanian sentence the "și" means that we also have that type of dessert, in addition to what may be on display or may have been previously mentioned, or you might not have yet seen in the store. A store owner could tell you that.
If it's in the context of dining, then it doesn't have to be in addition to what other people are having, it could be in addition to what we might have previously mentioned. If we told you that we are having steak and potatoes, we could add that we are also having chocolate dessert.
Correct, "Și noi avem desert" would mean "We too are having dessert" or "We as well," if you prefer.
Thanks. It would seem in this respect, Romanian is less ambiguous than English.
Yes, in this particular instance, although if you want ambiguity, deșert in Romanian means desert in English. :) And since diacritics can be a pain (I don't want to change my keyboard layout, but more recently I got more serious about my diacritics because I was curious whether I still remembered them; I found myself doing a lot of copying and pasting in my email messages), there can be quite a bit of ambiguity online as stated in this forum post:
Learning Romanian sucks a little without diacritics :( https://forum.duolingo.com/comment/19862451
Because Romanian on Duolingo is full of bugs, and the moderator is probably dead.