The answer to your specific question is NO, Active Directory does NOT allow spaces in DNS hostnames. The prohibited characters are clearly outlined in KB 909264 - Naming conventions in Active Directory for computers, domains, sites, and OUs in the section labeled Disallowed characters it reads:
The DNS host name cannot contain blank or space characters.
To extend the answer beyond Active Directory to the DNS domain name system in general the situation is a little trickier because while spaces technically are allowed in certain instances, in practice you will probably never encounter such a case yourself.
The short answer: DO NOT USE SPACES IN DNS HOSTNAMES!
The long answer according to §2 of RFC 3696, Restrictions on domain (DNS) names, is that:
Any characters, or combination of bits (as octets), are permitted in
DNS names.
It continues stating (emphasis mine):
However, there is a preferred form that is required by most
applications. This preferred form has been the only one permitted in
the names of top-level domains, or TLDs. In general, it is also the
only form permitted in most second-level names registered in TLDs,
although some names that are normally not seen by users obey other
rules. It derives from the original ARPANET rules for the naming of
hosts (i.e., the "hostname" rule) and is perhaps better described as
the "LDH rule", after the characters that it permits. The LDH rule, as
updated, provides that the labels (words or strings separated by
periods) that make up a domain name must consist of only the ASCII
[ASCII] alphabetic and numeric characters, plus the hyphen. No other
symbols or punctuation characters are permitted, nor is blank space.
If the hyphen is used, it is not permitted to appear at either the
beginning or end of a label. There is an additional rule that
essentially requires that top-level domain names not be all-numeric.
In practice this means you should NOT use spaces, even though in the most general specification of domain names as defined in these excerpts from §5.1 of RFC 1035 it is possible to allow spaces in domain names:
<domain-name>s make up a large share of the data in the master file.
The labels in the domain name are expressed as character strings and
separated by dots. Quoting conventions allow arbitrary characters to
be stored in domain names.
and
<character-string> is expressed in one or two ways: as a contiguous
set of characters without interior spaces, or as a string beginning
with a " and ending with a ". Inside a " delimited string any
character can occur, except for a " itself, which must be quoted using
\ (back slash).
Keep in mind that elsewhere in RFC 1035, specifically §2.3, it warns:
2.3. Conventions
The domain system has several conventions dealing with low-level, but
fundamental, issues. While the implementor is free to violate these
conventions WITHIN HIS OWN SYSTEM, he must observe these conventions
in ALL behavior observed from other hosts.
2.3.1. Preferred name syntax
The DNS specifications attempt to be as general as possible in the
rules for constructing domain names. The idea is that the name of any
existing object can be expressed as a domain name with minimal
changes.
However, when assigning a domain name for an object, the prudent user
will select a name which satisfies both the rules of the domain system
and any existing rules for the object, whether these rules are
published or implied by existing programs.
For example, when naming a mail domain, the user should satisfy both
the rules of this memo and those in RFC-822. When creating a new host
name, the old rules for HOSTS.TXT should be followed. This avoids
problems when old software is converted to use domain names.
I would certainly welcome further clarification or correction of my interpretation, but please do not do so unless you're able to cite specific sections of RFCs to either affirm or deny this interpretation.