I think legally you can do it. Actually, in a DV lottery case with a lawsuit, the applicant did exactly that. He took FPs at an authorized agency and submitted them.
Something needs to be done along these lines as USCIS is unable not only to timely adjudicate the applications but to schedule FP also.
From the USCIS website: Where are the Mobile routes?????????????????????????
Welcome to the Fingerprint Home Page. This Home Page provides information on the
fingerprinting services provided by USCIS to applicants.
USCIS requires applicants and petitioners age 14 to 79 for certain immigration benefits to be
fingerprinted for the purpose of conducting FBI criminal background checks. To better ensure
both the quality and integrity of the process, USCIS processes fingerprint cards for
immigration benefits only if an authorized fingerprint site prepares them. Authorized
fingerprint sites include USCIS offices, Application Support Centers (ASCs), designated law
enforcement agencies, and U.S. consular offices and military installations abroad. In general,
USCIS schedules people to be fingerprinted at an authorized fingerprint site after an
application or petition is filed. USCIS charges $70 per person (for most applicants) at the
time of filing for this fingerprinting service. Please check the instructions on your Immigration
application or petition form to find out if you must be fingerprinted.
To make fingerprinting more convenient for our customers, USCIS has opened a combination
of fixed and mobile fingerprint sites. In total, USCIS has opened 76 freestanding fingerprint
sites (ASCs) and 54 sites located in existing USCIS offices; established mobile routes
serving 46 points of service; and designated 45 law enforcement agencies to take fingerprints
for immigration benefits. USCIS is now working toward a system where fingerprints will be
taken and submitted electronically to the FBI. By using electronic fingerprint technology,
USCIS expects to significantly reduce processing times for criminal background checks.