It depends on how the program is run. If the company runs the program out of treasury stock (shares that are authorized, but not issued), then there aren't any shares being purchased on the open market. Because of that, the share price wouldn't be affected.
If you look in your employer's annual report, you will probably find how the program is run and how many shares are issued annually under that program. By comparing that to the daily trading volume of the company's stock you can gauge whether there's any likelihood of the share price being affected by the employee purchases. That is, of course, if shares are being purchased on the open market.
For example, here is Books-A-Million's program, as described in their 2011 annual report:
Employee Stock Purchase Plan
The Company maintains an employee stock purchase plan under which shares of the Company’s common stock are reserved
for purchase by employees at 85% of the fair market value of the common stock at the lower of the market value for the
Company’s stock as of the beginning of the fiscal year or the end of the fiscal year. On May 20, 2010, the stockholders of the
Company approved an additional 200,000 shares available for issuance under the plan, bringing the aggregate number of
shares that may be awarded to 600,000. Of the total reserved shares, 391,987, 373,432 and 289,031 shares have been
purchased as of January 29, 2011, January 30, 2010 and January 31, 2009, respectively.
This describes an instance of the employee purchase program being run from unissued stock, not open market purchases. From it, we can tell 18,555 shares were issued during the past fiscal year. As their average daily volume is ~40,000 shares, if the program were run from a single open market purchase, it would have potential to "move the market". One would think, though, that a company running it from open market purchases would spread the purchases over a period of time to avoid running up the price on themselves.