A rapid quadrupolar relaxation will lead to broad, poorly resolved lines in your spectrum. Since sensitivity is proportional to resolution, this will also decrease your sensitivity. However, there are reports of 105 Pd NMR spectra.
Try it and let us know. Use a very large SW to get a small dwell time. (so you can catch a broadisch signal). Your success depends on the species. for example 6Li gives very sharp signals. It depends on the electronic environment. A quadrupolar nucleus relaxes via field gradients. This is why you can do SO4 easily CS2 (more difficult) and pretty much have no success with most other S containing. So if the environment is symmetric you have a very good chance in getting it. Also it depends on the tumbling rate. Example Sc or Al ions are very broad, if they are bound to a protein then they become sharp.
Germann, M. W., Aramini, J. M. & Vogel, H. J.: A Quadrupolar Metal Ion NMR Study of Ovotransferrin at 17.6 Tesla. Journal of the American Chemical Society (1994), 116, 6971-6972. DOI: 10.1021/ja00094a076
Aramini, J. M., Germann, M. W. & Vogel, H. J.: Soft-Pulsed Aluminum-27 QCT NMR Studies of Ovotransferrin. J. Mag. Res. (1997), 209, 111-114. DOI: 10.1006/jmre.1997.1262