Can I charge a SLA battery with 13v?
If you have a circuit that is intended to run from a lead-acid battery, then yes, a 13 V power supply should power it without problems.  As you say, lead-acid batteries are often float charged at around 13.6 V, but are 12 V or less when being discharged.  Since 13 V is well within the expected range of a lead-acid battery, the circuit should be able to work with this voltage.

Added

I see now that you are asking about charging the battery with 13 V, not running the load with 13 V.

Yes, that will work somewhat, but won't charge the battery optimally.  Any voltage higher than the open-circuit battery voltage will charge it, and 13 V is high enough.  However, it can take a long time to really charge the battery fully.

Take a look at your 13 V power supply carefully.  There may be a output calibration adjustment in it somewhere.  If it's a "13 V" supply (odd value, but we'll go with that), then very likely it can be adjusted up to 13.6 V if there is any adjustment at all.

Another possibility arises if this power supply has a sense input.  It actually adjusts the output to regulate the sense input.  The purpose of a separate sense input (instead of just regulating the output directly) is to allow a remote node to be regulated.  You run a separate wire from that remote node to the sense input, and the remote node will be at the specified voltage.  The power supply puts out a little more as needed to overcome voltage drop in the wires, for example.

If your power supply has a sense input, connect a diode from the output to this sense input, and then some resistance to ground to make sure there is at least a mA or two going thru the diode.  The sense input will be at the output voltage minus the diode drop.  Since the sense input will be regulated to 13 V, you will get about 13.6 or 13.7 V at the output, which is perfect for charging lead-acid batteries.