The Magic Ratign rules from UA give some benefit for spellcasting, yes - in terms of caster elvel for SR, duration,r ange, etc. But not for spells per day.
A ranger (or paladin or bard) gets, from levels 1-20, a magic rating of [0/1/1/2/2/3/3/4/4/5/5/6/6/7/7/8/8/9/9/10/10] (note the simple pattern). Druids (or clerics, sorcerors, and wizards) get magic ratign equal to their class level. Everything else gets a pattern of [0/0/0/1/1/1/2/2/2/...].
Your caster level for purposes of everything except spellsper day and maximum spell level castable, is the sumof all your magic ratings.
So a Ranger(5)/Druid(5) would have a magic rating of 7; he would cast the same spells-per-day as any other druid(5), and as any other Ranger(5) ... but the duration, range, number of targets, damage, area, and SR penetration (etc) woudl all be based on a caster level of 7.
...
For what your player is looking for, the Prestige Ranger (also from UA) might be better. Prerequisites are BAB +4; Knowledge(nature) 2 ranks, survival 4 ranks; endurance, track, and either rapid shot OR two-weapon fighting; and lastly, the ability to cast calm animals as a divine spell.
The class gives all of the ranger's goodies over the course of 15 levels, in terms of class abilities. And ... every even-numbered level gives +1 spellcaster level! Thus, a Fighter(2)/Druid(3)/Prestige Ranger(15) would cast spells as a 9th level druid.
Animal Companion progression for hte Prestige Ranger is full druid rate, not the half-rate that rangers normally get. So the same example character woudl have the animal companion of an 18th level Druid.