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Java (OpenJDK 8), 9393 81 bytes

s->{booleanint w=falsew=0,p=w,l;for(char c:s){l="aeiouy"w|=p&(p=l="aeiouy".indexOf(c)<0;w=p&&l||w;p=l;}return!(w|p>>31);;return w+p>=0;}

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Java (OpenJDK 8), 93 bytes

s->{boolean w=false,p=w,l;for(char c:s){l="aeiouy".indexOf(c)<0;w=p&&l||w;p=l;}return!(w|p);}

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Java (OpenJDK 8), 93 81 bytes

s->{int w=0,p=w,l;for(char c:s)w|=p&(p=l="aeiouy".indexOf(c)>>31);return w+p>=0;}

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Java (OpenJDK 8), 93 bytes

s->{boolean w=false,p=w,l;for(char c:s){l="aeiouy".indexOf(c)<0;w=p&&l||w;p=l;}return!(w|p);}

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