According to ICANN: only if they have trademark rights in the label "alpha". (The label is defined as the word between the dots and is determined after illegal characters are resolved with nothing or a hyphen. This means that the trademark A_L_P_H_A and alpha both become just alpha for the purposes of this process.)
If another alpha trademark holder also tries to register alpha.bet the applicants will end up in the clearinghouse for resolution during the claims period which follows the sunrise period.
The Trademark Claims period follows the Sunrise period and runs for at
least the first 90 days of an initial operating period of general
registration. During the Trademark Claims period, anyone attempting to
register a domain name matching a mark that is recorded in the
Trademark Clearinghouse will receive a notification displaying the
relevant mark information.
See section 2.1 in the New gTLD Program: Trademark Clearinghouse memo. The clearinghouse is the system whereby the matches are identified and processed.
All Clearinghouse trademark comparisons occur by comparing the textual
elements of a mark with the second level label of the domain name
being registered. When all and only the complete and identical textual
elements exist in both the trademark and the label, it is considered
an identical match. For example, the trademark and the domain
label “ICANN” to be used in a domain name such as “icann.org” would be
an identical match.
If two entities both hold a trademark in the same gTLD label they ultimately end up in auction where the domain goes to the highest bidder. (Understanding Auctions).
If the bidder who wins ends up registering a site in an infringing manner it's up to the mark holder to resolve the dispute using their local courts.
