In Act 5, scene 2 of Hamlet, does Gertrude know that the wine is poisoned and drink it to save her son's life?

This is a great question! There is no specific textual evidence
to definitively say yes or no, but it makes for an interesting discussion of the subtext of the
play and what a director can do with looks, actions, timing, etc. to convey her knowledge or lack
thereof.

Based on the actual text of the play there is no direct
statement that she knows anything is amiss with the cup of wine. For the king to have the cups
out and to toast to his son would be standard form for the day, and his putting the "union" -- a
very large pearl which he claims 4 kings before him wore in the crown -- in the cup of wine would
have been a typical way to pass along the additional reward. It is kind of like a man putting the
diamond engagement ring in the glass of champagne at the proposal. These actions aren't all that
suspicious. Hamlet turns down the initial offer of a drink, and after the second touch by Hamlet
it looks like Hamlet is going to win the fencing match. At this point, Hamlet has been working
hard and looks thirsty and sweaty. Gertrude notices this and takes the cup and her napkin
(handkerchief) to Hamlet. The sequence of the lines really matters here: first she says "The
queen carouses to thy fortune, Hamlet." This means that she is lifting the cup in a toast to him.
He acknowledges the toast with saying, "Good madam!" The next line is Claudius's; he says,
"Gertrude do not drink." This implies that she is just about ready to take a drink herself and
she makes a sharp, potentially brash reply when she responds, "I will, my lord; I pray you pardon
me." This line could be delivered sarcastically, implying that she is enjoying her willful
defiance of the Claudius's command, thus showing Hamlet that she is doing what he wants and
trying to stay away from or stand up to Claudius. No matter how the line is delivered however,
the next implied action of the play is that she offers the cup to Hamlet who tells her, "I dare
not drink yet, madam; by-and-by." If she had known that the cup was poisoned, I don't think she
would have risked offering it to him if there was any chance he would have taken it from her.

Once she starts to feel the effects of the poison her dying words
are a warning directly to Hamlet that the cup was
poisoned.

Now to the supposition that perhaps she knew. Could she
have been suspicious of Claudius's suggestion of the duel and his glowing praise for Hamlet's
fencing abilities? Sure. Could she have noticed that Claudius drank from the cup and
then put the union in? Sure. Could she have found it odd or suspicious that Claudius
warned her not to drink for the cup, so she did so that Hamlet wouldn't? Sure. A director of the
play can only have those ideas played out with facial expressions on the queen's face, and
perhaps the pace and timing of the delivery of the lines. Shakespeare never wrote explicit stage
directions, so the reader has to read the intent of the lines with great
care.