Can you send someone a gift if they haven't opened the last one you sent?

I want to store gifts from far away friends until I have an open egg slot.

I'm curious if they will get an error if they try to send me a new gift the next day. (if I haven't opened the old one yet)

No, you can’t send someone a gift if they haven’t opened the last one you sent.

The ‘Send Gift’ button for them will be greyed out, and if they try to press it anyway they will get this error:

You able to wait and open gifts at your convenience, however your friends will not be able to send you another gift until you open the current one they sent.

Niantic Support

You can send each of your friends up to one Gift per day. If your friend has not yet opened a Gift that you’ve previously sent them, you won’t be able to send them