Battery capacity (unknown), load energy needs and PV panel wattage are needed for a full answer.
Most "12V" PV panels intended to properly charge 12V lead acid batteries have a Wmp = maximum Watts output in full sun, at Vmp = 17 to 18V. 15V Vmp would be unusual on larger panels intended for 12V LA use, but not inconceivable on smaller panels where the manufacturer "does not know and/or does not care".
Assume initially that a "constant wattage" load is available. This is not an essential assumption but removes unnecessary complexity from the example.
Assume initially that any diodes used have zero voltage drop when conducting.
If a 10 Watt load is applied to a PV (Photovoltaic) panel that is receiving enough insolation (solar input) to provide say 12 Watts at Vmp then the panel voltage will rise above its Vmp. If Vmp is say 15 Volts then, if a 12V "80% charged" lead acid battery is also attached to the panel.
If the panel available wattage falls below 10 Watts then if the battery is also connected, the battery will make up any shortfall.
If the battery continues to supply some or all of the load current the battery voltage will fall until it reaches a safe minimum level. If discharge continues past this point damage will occur and then substantial damage.
Once discharging reduces battery voltage to the safe minimum level the battery should be recharged as soon as possible. Holding the battery in a discharged state will cause progressive damage.
A PV panel with excess energy output potential will NOT be damaged if all potentially available energy is not used.
SM: ... it is easy to charge a battery with a solar panel and blocking diode, provided it is a lead-acid type the battery will not boil.
... whether this is safe depends on the size of the battery and the size of the solar panel. For small panels and large batteries it may be safe. But I would recommend using an over-voltage cutoff of some sort to protect the battery anyway.
SM: regardless, this configuration works.
SMs understandings are inadequate and/or wrong.
In some selected cases it is possible to simply connect a PV panel via a diode to a lead acid battery and obtain 'reasonable' results. In most real world situations this simple arrangement would be damagingly inadequate.
A suitably low energy charger MAY be able to be connected to a lead acid battery indefinitely without causing massive damage.
But, most charging systems which are designed to charge lead acid batteries in "sensible time periods" in "typical applications" will also substantially damage or destroy batteries if not managed correctly.
Added some years on:
Lead Acid batteries will have a manufacturer specified acceptable maximum trickle charge rate. This may be zero - but as led acid batteries have a self-discharge rate, a non-zero trickle charge current will usually be acceptable.
HOWEVER - 'this is not how it's usually done'.
Balancing trickle charge current against self discharge would be close to impossible if a current based approach was taken. Instead a lead acid cell is charged to a selected voltage, held there for a designed period to complete bulk or topping charging, and the voltage is then slightly reduced to an appropriate float charge level. By holding the battery at this fixed voltage the self discharge requirenments are utomatically met.
The use above of the vague terms 'selected', 'designed' and 'appropriate' is purposeful. While examples could be given, these vary with type of construction, size and use and it is highly desirable to obtain a manufacturer's figures for a given battery.
Battery University has much material on charging lead acid batteries, with this page being a good starting point.'
In the context of the present question, this means that the general statements I made some years ago still apply - non voltage-limited trickle charging is liable to cause damage.