I take it that your question is related to the manufacturing process and not to any specific compliance issues related to the European Union or China.
If the case of being able to manufacture parts (i.e. solder) to a lead free PCB by using lead based solder paste, the answer is YES you can do this.
Your solder joints will be adequate in regards to IPC610 specs and there should be no fine pitch solder issues provided the manufacturer doing the work for you is competant.
The two things to remember with this whole lead free issue in regards to a finished assembly is related to two items:
First the manufacturing issue is related more to the dwell time needed to get the solder paste to 'wet' up and reflow so that parts will attach to the PCB.
The second issue is that lead free parts (notice I did not say RoHS) will need to be completely 'dry' before being placed for manufacturing. What I mean by this is that they must be taken right from the dry pack they arrived in with in the time frame listed on the bag before needing to baked or they need to be baked before use. The reason here is that with the elevated temps, it is not uncommon for lead free parts to popcorn during the surface mount solder process.
Also dont let anyone tell you that you cannot use lead based paste for lead free parts or lead free paste with lead based parts or even mix lead free parts with lead based parts on an assembly. Many contract manufacturers have been doing this with great success.
Finally, in case anyone is really interested, this is not the first time lead free paste has been used. When electronic assembly first started being done lead free paste was used (late 1950s early 1960s). The reason we stopped was because we did not know how to control the wiskers that developed. To stop the wiskers we added lead to paste. The difference now is that we have learned how to make a lead free paste that does not wisker up as much.
Hope this helps.
E