Integrated sensing and communication (ISAC) enables simultaneous sensing and data transmission but exposes a critical vulnerability: probing signals may be intercepted, revealing both the transmitted information and the act of sensing itself. Existing physical layer security approaches mitigate interception yet operate with detectable signals, leaving sensing activity observable to a passive warden. This paper introduces sub-noise-floor pseudo-random probing (SNF-PRP), a covert sensing framework for OFDM-based ISAC systems under an energy-detection adversary model. SNF-PRP establishes an $ε$-covertness guarantee via Kullback-Leibler (KL) divergence, exploits an $N_{\mathrm{sc}}$-fold spreading gain absent from prior wideband analyses, and derives in closed form the minimum integration length required to achieve a target Cramér-Rao bound (CRB). Simulations under 5G~NR n78 numerology confirm sub-0.5\,m range and sub-0.5\,m/s velocity accuracy with KL divergence $5.8\times$ below the covertness threshold, validating joint feasibility at $-12$\,dB and $-15$\,dB probing powers.