I've been supporting my boyfriend for all of 2020 as he has been a full-time student receiving a housing allowance from his G.I. Bill for going to school. I did not withhold him on my W4. Can I still

Yes.

The number you claimed on your W-4 was just an estimate. You don't enter it anywhere on your actual return. It does not lock you in on what you can claim, at tax filing time. The IRS does not try to match that number with the actual number of exemptions you end up filing for.

That said, the next question is: does your BF qualify as your dependent.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable.  That is, it can only be used to reduce an actual tax liability.

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4300
3. The taxpayer (you) must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer

Nontaxable GI Housing money doesn't count as income, for the income test, but that money does count as support not provided by you, for the support test. 

The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants.

If he qualifies as your dependent, you may also claim the education tax credit for his tuition and other qualified expenses.   But, scholarships, student loans and GI educational benefits also count as support not provided by you for the dependent support test

To claim him as a dependent, her must live in your home the entire year, and you paid more than half his total financial support, and he has less than $4250 of taxable income.  

His total financial needs include room and board, clothing, tuition, travel, medical and so on.  The GI Bill does not count as taxable income but it does count as support he provides himself.  Support you provide includes the value of room and board if you pay for it (half your rent, utilities, food, etc.) plus any other financial support you provide.  

The W-4 does not lock you into anything when you file your actual tax return.