The rapid solar spikes (100--500 ms) recently discovered at submillimeter waves bring new possibilities to investigate energetic processes near the solar surface that might have an important role in the launch and propelling of ionized mass away from the Sun. We present a study on the association between the launch time of coronal mass ejections (CMEs) observed by the LASCO instruments on the SOHO spacecraft and the onset of the new kind of rapid solar spikes (100--500 ms) observed at submillimetric waves (212 and 405 GHz) by the new Solar Submm-wave Telescope (SST). We investigated six submm-wave events, all found associated to CMEs. Seven related CME were identified. Five of them were associated with flares with large GOES class soft X-rays, presenting distinct time histories and associations at other energy ranges, and two of them were related to flares behind the solar limb, with simultaneous related activity observed in the visible solar disk. Ultraviolet images from EIT on SOHO show some kind of small or large-scale magnetic activity or brightening for all events. The extrapolation of apparent CME positions to the solar surface show that they occurred nearly coincident in time with the onset of submm-wave pulses for all six events. These results suggest that pulse bursts might be representative of an important early signature of CMEs, especially for events beginning near the center of the solar disk, sometimes identified as halo CMEs. They lead to several challenging questions relative to the physical nature of the pulses and its association to the launch and acceleration of coronal mass ejections. Although these evidences may favor multiple rapid energy releases at the origin near the solar surface, they require further research in order to better understand both diagnostics and model descriptions.