でも not merely consists of で+も accidentally, it is a combination of で and も, and has then grown beyond the sum of its parts. Still, its meaning has not shifted completely, and so it should not be surprising that we can come across some phrases where both interpretations work. (Also それでも, it can be analyzed both ways.)
Note that this is not the でも that can go sentence-initial, "But...".
(Going slightly off-topic, it is my opinion that developing an understanding for how words and different meanings of a word are related helps to develop a feeling for the language.)
Perhaps not under any circumstances whatsoever, but 「スポーツをして汗をかいた後でも水分をとってはいけない」 is a pretty strong (negative) command, or introducing a rule the student is expected to observe. でも is responsible for "not even", てはいけない for the commanding part.
I am not certain whether asking if it is (by native speakers) analyzed as でも or で+も is a question that can answered objectively, but perhaps it might prove to be of interest to consider whether ~ででも is possible. If a speaker does not perceive the で in でも anymore, he might feel the need to insert the particle で again.
This has happened with 他の, and you can see people saying 「他のの」. For example, 「また、物の成分本質（原材料）が薬事法上食品に使用可能なものであっても、他ののいずれかが医薬品的であれば製品を「医薬品」と判断します。」