I think that much of the confusion here arises from phraseology and consideration of whether we are talking about the direction of sideslip when we apply the entry contols or once stabilised in the spin, and whether we are talking about attempting to induce a spin or one occurring inadvertently. The words "slip" and "skid" are old terms referring to the direction of any sideslip that is present during a turn. "Slip" is sideslip in the same direction as the turn ( i.e. relative airflow from the left of the nose in a left turn and vice versa) and "skid" is sideslip in the opposite direction to the turn. In, say, a left turn, left sideslip will invariably be present (certainly in light, piston-engined aircraft) if the turn is flown rudder free (i.e. without rudder co-ordination). So, the question is can you enter an intentional left spin from a left turn? Some aircraft you can, some you may not be able to. It depends on two factors: a. Is the rudder power available at entry sufficient to overcome the sideslip inherent in the turn and generate enough sideslip in the opposite direction to trigger autorotation? b. More importantly, if rudder is applied in the direction of turn, does the increase in IAS that results from the increased nose down pitch attitude due to the yaw rate resolved through the bank angle prevent the wing(s) from stalling? If the applied rudder generates a reasonable roll rate (due to lateral stability and Lr) the aeroplane probably will spin. If the resultant motion is a high yaw rate with roll, it may not. Remember not to confuse the direction of sideslip during a spin with the direction of sideslip at the point of pro-spin control application. Also, if in wings level flight there is no difference between slip and skid!
If you consider inadvertent spins, the slipstream effects from the prop and possibly gyroscopic moments and torque effects must be considered. Again, it will vary from aircraft to aircraft but it could occur.
Out of interest, the most stable intentionally entered spins in the Hawk (which has somewhat inconsistent spin characteristics) generally are achieved by entering from a 30 deg AoB turn in the direction of the spin.