Well, one thing for certain that happens no matter the version, is that after the summoning, Magus disappears from 600AD. Whether being sent to another time or outright killed, once word spreads the humans manage to turn the tide of the war and becomes the victors.
Crono and co.'s interference, whether it actually interrupted the ritual or not, did had an important impact: Magus now had to fight them instead of saving that energy for killing Lavos. What I think is, that without interruptions, Magus attempted to fight, which probably lead to Lavos killing him then. Interrupted and enduring being struck by the Masamune and the like, Magus wasn't in shape to do so, so that's why Lavos probably just sent the to different eras since no actual hostility presented itself towards it.
Also notice how despite Lavos being called forth, only a giant gate was opened. It's probable that it wasn't really Lavos being called to 600AD but instead Magus just opening a gate to it's dwelling. Hence why once everything was said and done, in both version it's just a matter of the gate being closed, so to someone who were to stumble into the room afterwards, nothing would seem out of the ordinary. Hence, why one could think the whole thing failed. It just left no evidence to suggest it did, hence it's the assumption they'd most likely jump to.