When saying “의” as a possessive marker is it usually pronounced as “에”?

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Yes.
의 is tricky to pronounce even to native Koreans.
Here's a explanation about 의.
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The pronunciation of ‘의’
1) At the beginning of a word, ‘의’ is pronounced as ‘의’
<example> 의사 : [의사] (doctor)
2) At the other part of a word, ‘의’ is pronounced as ‘의’ in principle, but being pronounced as ‘이’ is allowed.
<example> 민주주의 : [민주주의] or [민주주이] (democracy)
3) As a particle ‘의’ (which means "of"), ‘의’ is pronounced as ‘의’ in principle, but being pronounced as ‘에’ is allowed.
<example> 나의 손 : [나의 손] or [나에 손] (my hand)
4) In the syllables starting with consonants, ‘ㅢ’ is pronounced as ‘ㅣ’
<example> 무늬 : [무니], 희망 : [히망], 너희 : [너히]