You will undoubtedly get some mutations that affect the antibiotic resistance gene or some components of the replication machinery. However those plasmids will never be recovered upon transformation and selection, so are essentially invisible to you. But this is one reason why you can't mutagenize too heavily otherwise your population of transformable plasmids goes way down. (There are other reasons as well, including DNA damage induced by mutagenic treatment and creation of lesions that the cellular repair machinery acts on). 

The important question is how much you need to mutagenize so that you have some probably of finding interesting mutants, but don't create lots of linked secondary mutations in your gene that you need to screen out. You could do a pilot experiment with some easy to screen gene like lacZ and see how much you need to mutagenize in order to obtain some number of lacZ- mutants (say 1-5% mutants). There will be a much higher rate of mutations, the 1-5% only represent the inactivating mutations. This then gives you an estimate of an effective mutagenesis treatment. 

many thanks!!

what if the mutation frequency increases up to 4 mutations/kb?

That is probably still ok but I wouldn't go a much higher unless you don't mind sorting out all the extraneous mutations if you find a hit with an interesting phenotype.

You are very generous!

One more thing: do you think it is possible to know what % of plasmids will be filter out after transformation in bacteria with that level of mutation frequency ?

It may depend upon your method of mutagenesis but probably one to two logs reduction in transformation with chemical mutagenesis. 

By the way, error prone PCR is a very effective method of doing random mutagenesis of a specific gene. You can find an abbreviated protocol and some references here.

Crum, MA, BT Sewell, MJ Benedik. (2016) Bacillus Pumilus cyanide dihydratase mutants with higher catalytic activity. Frontiers in Microbiology 7:1264. doi: 10.3389/fmicb.2016.01264.