Will a reckless driving charge in VA suspend my PA drivers license?

First we need to see what Pennsylvania says about out of state convictions. A reckless driving charge can be different in each state, and some states may have different definitions on what constitutes a reckless driving.

§ 6146. Enforcement agreements.

The secretary may enter into agreements relating to

enforcement of this title, including, but not limited to:

(1) the Driver License Compact and any other agreements

to notify any state of violations incurred by residents of

that state;

(2) agreements to suspend or revoke the operating

privilege of Pennsylvania licensed drivers who are convicted

in Federal court or in another state of any offense

essentially similar to those enumerated in section 1532(a)

and (b) (relating to revocation or suspension of operating

privilege);

Then we need to look at;

§ 1532. Suspension of operating privilege.

(b) Suspension.--

(1) The department shall suspend the operating privilege

of any driver for six months upon receiving a certified

record of the driver's conviction of or an adjudication of

delinquency based on any offense under the following

provisions:

Section 3367 (relating to racing on highways).

Section 3714(b) (relating to careless driving).

Section 3734 (relating to driving without lights to avoid

identification or arrest).

Section 3736 (relating to reckless driving).

Section 3743 (relating to accidents involving damage to

attended vehicle or property).

So next we should see if a Pennsylvania reckless charge is similar to a Virgina reckless driving charge.

§ 3736. Reckless driving. (Pennsylvania Law)
(a) General rule.--Any person who drives any vehicle in
willful or wanton disregard for the safety of persons or
property is guilty of reckless driving.
(b) Penalty.--Any person who violates this section commits a
summary offense and shall, upon conviction, be sentenced to pay
a fine of $200.

§ 46.2-852. Reckless driving; general rule. (Virginia Law)

Irrespective of the maximum speeds permitted by law, any person who drives a vehicle on any highway recklessly or at a speed or in a manner so as to endanger the life, limb, or property of any person shall be guilty of reckless driving. 

As you can see the vehicle code in Pennsylvania is very much like the vehicle code in Virginia.