No - Bathilda’s corpse was “animated” by Nagini in it, not magic.
An Inferius is a corpse reanimated by magic. Bathilda’s corpse was not animated by magic, it was animated by Nagini being inside it. The corpse only seems to be moving because Nagini was moving it, and it was incapable of doing anything that she couldn’t do, like cast spells or speak English. “Bathilda” was able to speak, but only in Parseltongue. It’s fairly clear from its behavior that Nagini is in control of the actions the Bathilda-corpse takes. She lures Harry away to converse in Parseltongue without him knowing, is told by the Dark Lord to keep Harry from leaving, then bursts out of the corpse to obey his command.
“Then she closed her eyes and several things happened at once: Harry’s scar prickled painfully; the Horcrux twitched so that the front of his sweater actually moved; the dark, fetid room dissolved momentarily. He felt a leap of joy and spoke in a high, cold voice: hold him!”
“And in the instant that he looked away, his eyes raking the tangled mess for a sword hilt, a ruby, she moved weirdly: he saw it out of the corner of his eye; panic made him turn and horror paralysed him as he saw the old body collapsing and the great snake pouring from the place where her neck had been.”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
She’s able to contact the Dark Lord, tell him Harry was there, and obey his command to her.
“She didn’t want to talk in front of you, because it was Parseltongue, all Parseltongue, and I didn’t realise, but of course, I could understand her. Once we were up in the room, the snake sent a message to You-Know-Who, I heard it happen inside my head, I felt him get excited, he said to keep me there … and then …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
For comparison, Professor Snape defines an Inferius as a corpse reanimated by a Dark wizard’s spells. Bathilda’s corpse was used as a puppet, but was not reanimated by spells.
“The Inferius is a corpse that has been reanimated by a Dark wizard’s spells. It is not alive, it is merely used like a puppet to do the wizard’s bidding.”
- Harry Potter and the Half-Blood Prince, Chapter 21 (The Unknowable Room)
Once reanimated, Inferi can “function“ on their own. However, Bathilda’s corpse collapsed to the floor, inactive, once Nagini came out of it.
Therefore, it seems most logical from the evidence that Nagini just wore Bathilda’s corpse as a disguise, like an outer shell to conceal herself, rather than the corpse being an Inferius or itself reanimated.