I would say no, it is not necessary, in that I ran the module and did not use this rule... but I'm not claiming we played it as it was intended.
A third level cleric going into this module has a maximum of two cure light wounds spells, for 2-7 points each. The party may have a potion of healing or two, but probably not much else. That is not enough to keep a whole party healed up unless several days are spent holed up on a secure location. Normally if you get too beat up, you can leave the dungeon and return to a safe camp or to town, but in this module you cannot.
Further, you are invading a family's house. The family knows every room in the house, and will know if you barricade yourself in somewhere. We are told they are eager to test and harass the party (out of boredom), and given that they are high level characters, its going to be difficult or impossible to keep them out, if they are determined to get in.
In this module the party is outmatched and must be clever, if they are to survive. A good DM will play on the family politics and quirks.
Now, I didn't use this rule, but my party was 6th level, and I was running it in D&D 3.0, so they had vastly more resources. They were goal-driven and went straight through, avoiding fights and unnecessary exploration. Also, I let them move room to room, and did not do much with the Amber family; they didn't move around, look for them, or act particularly intelligent. So a great deal will depend on your DMing approach as well as your player's approach, and on what D&D edition you are playing.
On a side note, the Amber Light is a foreshadow. Going into the castle they don't know about Stephen. They know they are trapped but not how to escape. Everyone seems crazy and against them, but the glowing light is a clue that they have an unknown ally. Stephen knows his family's oddities; he is powerful enough to protect the party; and he is motivated to be rescued. It would be odd if he did NOT help them in whatever way he could.
It is also interesting that in module X4, also written by Moldvay, there is an "unknown benefactor" that occasionally provides aid if the party gets into trouble.
NOTE: My original answer incorrectly stated that by the rules, you could not heal or regain spells without leaving the dungeon. SevenSidedDie corrected this in the comments. But my point was that if played as intended, the light may be necessary; even with the rules correction I think that is true. So I have edited this answer instead of deleting it.