Yes you can but the results may not be as you expect. The 555 can only supply a relatively small current and the maximum power it can drive into the transformer will be limited to approximately the 555 supply voltage multiplied by that current. What you get out of the transformer will depend on the ratio of turns on the primary (555 side) and secondary sides. It will step the voltage up if there are more turns on the secondary but it will not give you more power. In fact it will be quite a lot less than you put in to it.
Example: 555 produces 100mA at 5V output so the power to the transformer is (0.1 * 5) = 0.5W.
If the secondary had enough turns to step the voltage up to 250V, and the transformer is say 70% efficient, the output power would be (0.5 * 0.7) = 0.35W but you would only be able to draw 1.4mA from it.
Brian.