Yes, 3234.net can receive emails.
Yes, 3234.net seems to be a legitimate domain.
A record
13.32.181.36
MX records
alt1.aspmx.l.google.com
64.233.186.27
alt2.aspmx.l.google.com
209.85.202.27
aspmx.l.google.com
172.217.197.27
aspmx2.googlemail.com
64.233.186.26
aspmx3.googlemail.com
209.85.202.26
aspmx4.googlemail.com
64.233.184.26
aspmx5.googlemail.com
74.125.128.26