Yes, but for the sake of our argument we can treat the Time Egg's as if they are similar since they all do have some power over time.
So we can say that in the 3 main instances of Time Travel to the DBT, a Time Egg was used in only one of those (Chrono Cross). So it's likely not a requirement to travel to the DBT. In Cross it only opens the Gate to the DBT after all. Perhaps a Gate Key could have done the same thing?
Similarly, as I showed above, Schala's pendant is present in two of those cases (but not in Cross as we originally thought) so it holds more favor as being necessary to travel to the DBT.
Likewise, dimensional travel occurring beforehand happened in two of the cases of travel to the DBT, so it has an equal probability as Schala's pendant of being important.
Now, if the Time Egg that Belthesar gives the party in Cross is actually made out of Dreamstone, then one could say that some Dreamstone artifact was present in all three instances of travel to the DBT. Perhaps it has a similar effect as Schala's pendant, which is also made from Dreamstone and also has power over time.
EDIT: I just realized that in the New Ocean Palace incident, Schala uses the last of her Pendant's energy to warp the party away to safety, which leaves her Pendant drained and worthless. Can it even be considered as being "present" during her travel to the DBT then, since it is a non-functional artifact at that point?