Generally, yes. IRS 501(c)(3) recognition is (usually) effective retroactively to the earlier of 1) the organization’s legal formation or 2) the commencement of its programs. This means that the organization’s activities are retroactively tax-exempt and donations are retroactively tax-deductible to the donor, extending even to prior tax years. In order for the program-commencement date to be considered the effective date of tax-exemption, however, there must be an organizing document of some kind. Signed minutes from an initial organizing meeting of the board of directors may be sufficient. Under certain circumstances, IRS tax-exemption may only be retroactive to the date of the filing of Form 1023. This is particularly true for organizations formed more than 27 months prior to applying for 501(c)(3) status.
The bigger issue here is state compliance concerns. Most states require nonprofits to register with that state’s Division of Charities (or similar department) prior to any fundraising activities.