Was the word "even" said with one syllable? Many lines that contain the word "even" seem to have an extra syllable. ("Even when their sorrows almost were forgot").
The answer to your question is "yes", but only if you assume that Shakespeare's actors emphasised the iambic pentameter in speaking the verse. I'm not sure that they will have done, any more than we do now (i.e. not really at all).
Shakespeare's verse fits basically the template of iambic pentameter
de dum / de dum / de dum / de dum / de dum
But, you're right, some lines and words don't fit comfortably on that grid.
Evn WHEN / their SOR- / rows AL- / most WERE / forGOT
Speak it out like that, and 'even' has to squash into one syllable to make it into a regular line. But you also have to stress 'WERE' (unusual, if not ungrammatical!) and stress the first beat of 'almost' (we don't really do it) and, particularly, the last syllable of 'forGOT' (we definitely don't do it) to make it regular. It isn't just 'even' that's the problem.
Bottom line is that I don't think Shakespeare's actors would have pointed out the rhythm like that - and that part of the tension and energy comes from the way that rhythm continues underneath, but is not always observed. So it just depends. I don't think you can draw inferences about Elizabethan pronunciation from the way that Shakespeare versifies.
That's the theory. And it works in practice. Here's Cleopatra:
I will be even with thee, doubt it not
Here's Rosalind, from As You Like It:
Peace, I say. Good even to thee, friend.
And here's Mark Antony from Julius Caesar:
Octavius, lead your battle softly on
Upon the left hand of the even field.
What do you notice? In each case, the word "even" scans with two syllables. So don't worry about it - iambic fundamentalism isn't Shakespeare's way.
Hope it helps!