Following paper Tourette’s Disorder. Lyon, G.J., Shprecher, D., Coffey, B. et al. Curr Treat Options Neurol (2010) 12: 274. doi:10.1007/s11940-010-0073-x provides a good (somehow recent) review on Tourette's disorder and its therapeutic management.
Indeed, antihypertensive therapies are considered as potential therapeutic management in TD.
One recent open-label, prospective 8-week study of guanfacine (at an
average dose of 2.0 ± 0.6 mg/d) enrolling 25 medication-free
participants (23 males and two females), ages 7–16 years, showed a
mean improvement of 27% on the Hyperactivity Index, 32% on the total
score of the teacher-rated ADHD Scale, and 39% on the total tic
severity scale.
As I don't know whether this review in open access or not, here some extracts which may bring some clarifications:
Alpha-2 adrenergic agonists
Drugs in this class have demonstrated efficacy for both tics and ADHD
in randomized clinical trials, so this class is a good first-line
choice for patients with both conditions.
There is class I evidence for efficacy of oral clonidine [3, Class I]. Guanfacine is used in clinical practice with similar efficacy, a
more favorable side effect profile, and more convenient (daily or
twice-daily) dosing.
One class I study has now demonstrated the efficacy of the clonidine
transdermal system (patch) for tic disorders.
Standard dosage
Guanfacine (1 mg tablets) can be started at one half tablet at bedtime
and increased by half a tablet every 3–7 days until the maximum dose
of 4 mg per day is reached. Extended-release guanfacine is now
available in nongeneric formulation. For those who fail to tolerate
guanfacine, treatment with clonidine in adults can begin with one half
of a 0.1-mg tablet at bedtime, increasing the dose by half a tablet
every 3–7 days until the target dose of one half to one tablet two to
three times a day is reached. The maximum dose is typically 0.4 mg
daily in divided doses. Starting doses for clonidine and guanfacine in
children can be half of adult doses.
Contraindications
Known hypersensitivity to the product.
Following extract adresses your concern about low blood pressure
Main side effects Both clonidine and guanfacine are associated with sedation, fatigue, and somnolence. Reductions in heart rate and
blood pressure are modest and rarely lead to discontinuation of
treatment.
Obviously according to several studies, the clonidine/guanfacine doses used in TD are not associated with a significant drop in BP. Initiation of the therapy should be undertaken by your treating doctor who will undertake some follow-ups to ensure that you are not suffering from any side-effects.