Usually yes. But test it thoroughly.
Details below might be more applicable to restoring older equipment than a 2000s mainboard.
Some linear regulator ICs rely on capacitors being somewhat lossy - eg some low drop types that specify 10uF or 100uF ordinary electrolytics in their datasheets can become unstable (oscillate) if you substitute in MLCC or high quality tantalum capacitors. Super low ESR types could cause similar upsets.
Theoretically, a switching regulator design could have similar traps, or even use ESR as a peak current limiter.
Also, there might be cases where undocumented specifications (thermal mass? insulation capabilities of the package?), or tolerances to running out of specification, might have been taken advantage of.
Mind that some electrolytic capacitor juices are flammable, others are not. Substituting in a type with flammable juice where the original was intentionally chosen differently due to there being a perceivable catastrophic failure mode could raise a safety concern.
DO NOT substitute any TANTALUM types where there was not originally tantalum. Even avoid substituting tantalum with tantalum unless it is in well current limited circuitry. Example of NOT well current limited: The common 1980's practice of having tantalum capacitors across power rails as decoupling- these are best summarily replaced with normal electrolytics and MLCCs in combination. Also, don't reuse tantalum types once desoldered. Rationale: The common "dry" tantalum type (the teardrop or SMD-diode-like part) tends to fail short if it fails. If it does so while being able to draw amps of current, flares and explosions happen. And mishandling (overheating, mechanical stress...) worsens the chance of failure. The "wet" tantalum type will be rare (not to be found on a computer mainboard really) unless you are handling aerospace/milspec equipment - they are not so fragile and you should usually leave them alone if there are no problems, however be aware they are filled with literal sulfuric acid and can cause ample damage if they leak.