If *h1 were a glottal stop, and virtually all German word initial vowels have implicit glottal stop then would the claim about regular laryngeal loss have to be revised?
There's a rather recent development from the Hittite camp led by Kloekhorst claiming (see Laryngeal_theory) that *h1 may have been a glottal stop. Assuming that were true, ignoring the other Laryngeals for the moment, and assuming that glottals were never signed in western alphabets, this would mean that we can hardly tell whether Laryngeals were lost. We don't know how precise the Laryngeal theory is, of course. If all Germanic vowel-onsets include a glottal plosive1, then there's no particular significance to finding words among them that are reconstructed with the laryngeal. At least that fact doesn't negate the claim either.
So, I need to know what show stoppers to look out for, before searching for the coincidence of a PIE-German pair fulfilling this constraint, which shouldn't be hard to find. Any other IE language that is not aspirated, if that's the principal divide, would also work. Primarily, if the glottal plosive vowel onset is evidently an innovation, then the whole idea would be junk.
1: Calling an onset a stop is just counter-intuitive. Tangentially to the phonetics, Arabic for example notes hamza, which wt:de:Hamza equates to the sound in German beachte [bəˈʔaxtə], though I was under the impression that there's a slight difference. My Arabic is certainly weak. ayn is also a noteworthy tangent, because that's a pharyngeal, though that's a different matter.
PS: One example might be *h1er-, "earth".
Compare that to George, supposedly from γῆ (gê) "earth" + ἔργον (érgon), PIE *werǵ- "work". The root of γῆ is uncertain, supposed to be "Pre-Greek" or "Pre-Proto-Indo-European". So there'd be more at stake than internal reconstruction, if *h1er- and *werǵ- should relate via George. Note that Personal names are frequently subject to folk etymology. Possibly related, *h₂éǵros gives agros "field, achre" (agrarian etc.); Indeed, wiktionary links *h1er- to *h₂erh₃- "to plough".