Yes, if they want to make the election to treat the nonresident Alien spouse as a Resident, they can make that election (see link) and file a Joint tax return.  However, they do need an ITIN.

https://www.irs.gov/publications/p519#en_US_2018_publink1000222196

https://www.irs.gov/credits-deductions/individuals/how-do-i-apply-for-an-itin

Filing as Single is not an option.  If they don't file a Joint return, the client would file as Married Filing Separately (or possibly Head of Household if there is a qualifying dependent).