Short answer. No. The rule listing the orders in special proceedings that may be appealed contains an express carve-out: no appeal shall be allowed from the appointment of a special administrator. Other orders in the same estate proceeding may still be appealed, so the bar is specific to this one appointment.
What the law says
except that no appeal shall be allowed from the appointment of a special administrator
Rule 109, Section 1 — Orders or judgments from which appeals may be taken. Read the full provision →
An exception written into the appealable category
The rule allows an interested person to appeal an order that constitutes, in proceedings relating to the settlement of a deceased person's estate or the administration of a trustee or guardian, a final determination in the lower court of the rights of the party appealing. The carve-out sits inside that very clause. So the appointment of a special administrator is not merely absent from the list — it is pulled out of a category it might otherwise have fitted, which is a stronger signal than silence would have been.
Why this particular order is treated differently
A special administrator's role is a stopgap. The appointment is made to keep an estate from sitting unattended while the larger questions are being resolved, and it is by its nature provisional rather than a settled allocation of anyone's rights. Allowing an appeal from it would let the interim measure be suspended by the very dispute it exists to bridge, which would defeat the reason for making it quickly in the first place.
What remains appealable in the same case
Do not read the carve-out more widely than it is written. The rule lists several orders an interested person may appeal in special proceedings: one that allows or disallows a will; one that determines who are the lawful heirs or the distributive share to which a person is entitled; one that allows or disallows a claim against the estate; and one that settles the account of an executor, administrator, trustee or guardian. Those are unaffected by the exception.
If you object to who was appointed
The unavailability of an appeal does not mean nothing can be said about an appointment you consider wrong. It means an appeal under this rule is not the route. What is open depends on the ground of your objection and on the stage the proceeding has reached, and those are questions to put to a lawyer with the order in hand. It is also worth watching for the final order or judgment in the case, which the rule lists as appealable where it affects the substantial rights of the person appealing — though even there the rule excepts an order granting or denying a motion for new trial or reconsideration.