Expanded Repertoire (Ex): At 2nd level and every four levels thereafter, a magician can add one spell to his spells known from the spell list of any arcane spellcasting class. The spell must be of a level he can cast. This ability replaces versatile performance.
Choosing spells from the spell list of an arcane spell-casting class which gets less spells at lower levels is mildly cheesy, but RAW legal since it's not a big enough issue to draw faq/errata attention.
I would say absolutely yes, it does allow this.
Honestly, it is far from game breaking, at:
2nd lvl the bard adds a 1st lvl spell
6th lvl the bard adds a 2nd lvl spell (haste at CR 6 isn't overpowered, summoner's get this at 4, wizards at 5)
10th lvl the bard adds 3rd or 4th lvl spell (black tentacals at 10th, isn't fast, summon monster V as 4th level spell is just amusing, but still slower than wizard's at class level 9)
14th lvl Bard adds 5th or lower when dedicated casters have 7th level spells... (Spell turning on the Summoner list is handy here)
I also wouldn't consider this "cheesy" so much as "the whole point or the Magician bard"
Legal. And not game-breaking in the slightest, since summoners and bards both use the same casting progression.
The Samsaran Mystic Past Life racial trait does the same thing and lets wizards poach from the Summoner spell list, though, and that does lead to silliness like getting access to high-level spells four levels early.