It seems to end up in their iCloud calendar instead of their Google Calendar.
I use Google Calendar and have had some problems receiving invitations from people using iCloud calendar (I have an iCloud account but I don't use the calendar). I therefore did some experimenting to try to nail down what was going on:
I created an event on iCloud and then invited my Gmail address. Nothing happened. I never received the invitation.
I created an event on iCloud and then invited a secondary Google Calendar I use (that is [random string]@group.calendar.google.com) address. Nothing happened. I never received the invitation.
From a second Gmail account I have I sent an invitation to the secondary Google Calendar in  above. It worked as expected.
Some additional details:
My main login to iCloud is a "subaddressedformed" version of my main Gmail address (something like email@example.com). I have also registered firstname.lastname@example.org (i.e., my main Gmail address in its basic form) as an account for sending and receiving iMessages.
I haven't tried hard to reproduce this but what I think happens when a friend invites from her iCloud calendar is that she enters email@example.com in the invitee-field in her calendar app on her iPhone and then iCloud somehow interrupts this invitation rather than sending it to my Gmail account.
How is this supposed to work?
It feels like a bug but there should be millions of people sharing this scenario.
I just figured out that there is a toggle in Calendar Settings on iCloud.com. If you have an iCloud account with a gmail.com email address, iCloud will indeed eat invitations sent from other iCloud accounts. But, if you go to iCloud.com > Calendar > click the gear in the lower left > Advanced > there is a toggle at the bottom of the pane for whether you want iCloud to receive invitations, or for an email to be sent to the gmail.com email address.
I can confirm that an Apple ID with gmail.com as the email will receive iCloud appointments and invitations. I dondid know if that means that google calendar is where this falls down or if that works, since the people I share calendars and calendar events use iCloud and calendar app primarily.