No, it doesn't work like that. The OML is applied if the holder of a CPL or ATPL becomes unable to meet the Class 1 requirements. The relevant passage in JAR-FCL 1 reads -
"The limitation ‘valid only as or with qualified co-pilot’ is to be applied when the holder of a CPL or an ATPL does not fully meet the class 1 medical certificate requirements but is considered to be within the accepted risk of incapacitation (see JAR–FCL 3 (Medical), IEM FCL A, B and C). This limitation is applied by the Authority in the context of a multi-pilot environment. A ‘valid only as or with qualified co-pilot’ limitation can only be issued or removed by the Authority."
A student pilot or the holder of a PPL would not have an OML applied because it is applied "....in the context of a multi-pilot environment". A pilot may have restrictions placed on his Class 1 or Class 2 medical, which may or may not prevent him from flying solo but it won't be an OML.