Dont think so - the concept of battery draining is nowhere related to eSim. There is no going back and consuming more battery with eSim.
Thanks for asking this though. it made me curious and i found out this...
Increased battery life: eSIMs are more efficient than traditional SIM cards, which means they use less power and don't drain your battery as quickly when connecting to the wireless network.
No, using eSIMs does not cause battery drain. Indeed, eSIMs are known to be more efficient than traditional SIM cards and to use less battery power. eSIM technology can even lead to longer battery life because it uses less power and drains less when connecting to wireless networks.