Will Deplin work without the use of an antidepressant? I was prescribed Deplin to help with PMDD?

Deplin is used together with anti-depressant medications in people with major depressive disorder (including PMDD) and low folate levels.
Deplin alone, in this instance, is unlikely to be of benefit in helping with PMDD unless you are folate deficient.
See: http://www.drugs.com/mtm/deplin.html

This from http://www.drugs.com/enc/premenstrual-dysphoric-disorder.html
"... Women with PMDD may be helped by the following:
A balanced diet (with increased whole grains, vegetables, fruit, and decreased or no salt, sugar, alcohol, and caffeine)
Adequate rest
Regular exercise 3-5 times per week
In addition, it is important to keep a diary or calendar to record the type, severity, and duration of symptoms.

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Selective serotonin-reuptake inhibitors (SSRIs) are antidepressant drugs that can treat PMDD. SSRIs include fluoxetine (Prozac, Sarafem), sertraline (Zoloft), paroxetine (Paxil), fluvoxamine (Luvox), citalopram (Celexa), and escitalopram (Lexapro).

Nutritional supplements -- such as vitamin B6, calcium, and magnesium -- may be recommended. Pain relievers such as aspirin or ibuprofen may be prescribed for headache, backache, menstrual cramping and breast tenderness. Diuretics may be useful for women who have significant weight gain due to fluid retention."