No, it absolutely shouldn't because that's just incorrect grammar. All modal verbs (those are words like can, could, should, would, may, might and a whole slew of others), at least in Modern English, knock out all the s's on the ends of the verbs that immediately follow them (as well as all the to's). In other words, modal verbs should only be followed by bare infinitives. Here's a simple example:
He should help me. (That's how you should say it.)
He should helps me. (No words can describe how patently wrong this is. There should be no s on the end of the verb help.)
The only time you tack an s on the end of a verb is when it is the first verb that immediately follows the subject in third-person singular form (those are typically singular nouns and the pronouns he, she, it and one). For example:
He likes to eat ice cream.
As for the sentence itself, it's fine as far as English is concerned. I think what we've got here is called a subjunctive form in a conditional sentence. The sentence would definitely be easier to read, if we put a comma after the word myomas:
Should the ultrasound demonstrate myomas, I will discuss her case in our meeting.
This is grammatically and structurally the same as saying the following:
Should you have any problems, let me know.
That's a very common phrasing in English and one way to understand this construction is to substitute should with if:
If you have any problems, let me know.
If the ultrasound demonstrates myomas, I will discuss her case in our meeting.
Best Answer
Although what we need are is possible in some cases, in this case it's a poor choice. Why? Because all three what we needs refers to the same thing, and that thing is either singular or plural, not both. It's quite strange to refer to it first as though it's plural, then as though it's singular.
The best choice is to use is all three times:
The parallelism is stronger rhetorically in any case.
Besides which, is is the more common choice overall. Take a look at this chart of four n-grams in the Google Books corpus:
From this chart, it seems that is is eight times more common than are; and specifically with negatives, it's ten times more common. So both occur, but is is clearly favored.