One-Time Use Randomized Number - sql

Question

Tables(columns) that are important here (there are more in my actual DB but I simplified):
Patients(PatientID, PatientNumber, DOB, Weight, RandomCode)
RandomNumbers(RandomNumberID, Available)
Sites(SiteID, SiteNumber)
Patients does not contain any data and is to be populated via a 3rd party GUI. RandomNumbers contains 50 entries. When a patient's data is first added to Patients, a random number 1-50 is selected, which is tied to RandomNumberID. The "available" column in RandomNumbers is treated as a boolean (T meaning available, F meaning unavailable). After the RandomNumberID is tied to a patient, that RandomNumberID cannot be used again (Available is switched to "F"). If an already used RandomNumber is assigned to a patient upon data entry, another randomly selected RandomNumberID is selected until one is found where Available is T.
Here is the storedproc that I've written so far:
GO
CREATE PROCEDURE uspPatientEntry
#intPatientID AS INTEGER OUTPUT
,#intPatientNumber AS INTEGER
,#intSiteID AS INTEGER
,#intRandomCode AS INTEGER
AS
SET NOCOUNT ON
SET XACT_ABORT ON
BEGIN TRANSACTION
SELECT #intPatientID = MAX (intPatientID) + 1
FROM TPatients TP (TABLOCKX)
SELECT #intPatientID = COALESCE(#intPatientID, 1)
SELECT #intPatientNumber = CONCAT(#intSiteID, #intPatientID)
INSERT INTO TPatients (intPatientID, intPatientNumber, intSiteID, intRandomCodeID)
VALUES (#intPatientID, #intPatientNumber, #intSiteID, #intRandomCode)
COMMIT TRANSACTION
GO
And here is another function I wrote to test it out:
DECLARE #intPatientID AS INTEGER = 0;
DECLARE #intSiteNumber AS INTEGER = 0;
DECLARE #intPatientNumber AS INTEGER = CONCAT(#intSiteNumber, #intPatientID);
DECLARE #intRandomCode AS INTEGER = FLOOR(RAND()*50)+1; -- This just picks a random integer 1-40. <- this is the heart of my question
EXECUTE uspPatientEntry #intPatientID OUTPUT, #intPatientNumber, 2, #intRandomCode
Would something like this work? Ignore syntax, just the general idea:
DECLARE #intRandomCode AS INTEGER;
SELECT #intRandomCode = FLOOR(RAND()*50+1;
FROM TRandomCodes TRC
WHERE TRC.blnAvailable = "T"
UPDATE TRandomCodes TRC
SET TRC.blnAvailable = "F"
WHERE #intRandomCode = TRC.intRandomNumberID;
Thank you