The Chasam Sofer explains why Eliezer insisted not to eat until he speaks first.
Eliezer suspected Besueil of wanting to poison him and by doing so Yitzchok will not be allowed to marry any woman in the world based on the Gemoro
האומר לשלוחו צא וקדש לי אשה סתם אסור בכל הנשים
(בקש לעקור את הכל)
This Halacha is only applicable if he tells him to be MekadeshIf he specifies to take a woman from a specific place or family then he may marry women from other places or other families.
Eliezer’s intent to speak before the meal was to tell Besueil there
is no point to poison him because Avrohom was very specific to find a wife from his own family. Even if Eliezer will die, Yitzchok will be allowed to marry other women.